D ) CatDog Matrix Multiplication 1 3. b) syms x y z NOTE. To better manage memory and prevent unnecessary memory allocations, Matlab uses: The negative of a matrix is also simple: These are the calculations: −(2)=−2 −(−4)=+4 False Problem 2. To display ‘Question 2’ in the command window, the correct command is 4 1. is a matrix with only 1 row : A = [5 4 3] 1 X 3 matrix. A = EMBED Equation.3 a 2 X 3 matrix
with 2 rows and 3 columns
component aij in the matrix is in the ith row and the jth column
e.g. If the order of matrix A is . is a matrix with only 1 column : A = 3 X 1 matrix. Matrix Multiplication 2 4. Algebra 2 Practice Test on Matrices 1. Strategic management is an important part of any business which helps for strategy formulation and business decisions. The Identity Matrix 5. The 2 2× matrix C represents a rotation by 90 ° anticlockwise about the origin O, Ans: a, 33. Students can solve NCERT Class 12 Maths Determinants MCQs Pdf with Answers to know their preparation level. MCQS MIDTERM EXAMINATION ~“LIBRIANSMINE”~ Question No: 1 (Marks: 1) - Please choose one If for a linear transformation the equation T(x) =0 has only the trivial solution then T is One-to-one Onto Question No: 2 (Marks: 1) - Please choose one Which one of the following is an elementary matrix… |A| = a21.C21 + a22.C22 + a23.C23
= (4.-11) + (3.4) + (7.6) = 10
Now we can find the Inverse��
A-1 = EMBED Equation.3
Step 1�: write matrix of co-factors
EMBED Equation.3 = EMBED Equation.3
Step 2�: transpose that matrix (replace rows by columns), so
EMBED Equation.3 = EMBED Equation.3
Step 3: multiply each element by EMBED Equation.3
A-1 = EMBED Equation.3 = EMBED Equation.3
So A-1 = EMBED Equation.3
Check�: A.A-1 = I
Practice inverting various 2X2 and 3X3 matrices using examples from Jacques, or other similar text books. Ans: c, 10. Matrices Multiple Choice Questions & Answers for competitive exams. Are you on the lookout for an Excel Matrix to present your business data? e) none of the above IndianStudyHub offers many fully Matrix | Data Structure MCQs pdf free download questions and answers with explanations. b) 12 divide each element by ad� bc)
If |A|=0 then there is no inverse��(matrix is singular)
Example�.find the inverse of matrix A
A = EMBED Equation.3
|A| = ad�bc = (1.4)�(2.3) = �2(non-singular)
A �1 = EMBED Equation.3 = EMBED Equation.3
Check�: A.A-1 = I = EMBED Equation.3
Example�.find the inverse of matrix B
B = EMBED Equation.3
|B| = ad � bc = (2.10) � (4.5) = 0
therefore, matrix is singular and inverse does not exist
Example Expenditure model of national income
Y = Income
C = Consumption
I = Investment
G = Government expenditure
Y = C+I+G (1)
The consumption function is
C = a + bY (2)
Note C and Y are endogenous. d) gravity D ) string theory columns
Identity Matrix I: AI = A and IA = A
I = EMBED Equation.3 (for 2 X 2 matrix)
Inverse Matrix�A-1: A.A-1= I� A-1.A= I
To invert 2 X 2 Matrix��
If A = EMBED Equation.3
Get Cofactor Matrix: EMBED Equation.3
Transpose Cofactor Matrix: EMBED Equation.3
multiply matrix by EMBED Equation.3 so EMBED Equation.3 (i.e. Reply Delete. Strategic Management Prepared by: CHUOP Theot Therith 2 a. potential entry of new competitors b. bargaining power of suppliers c. development of substitute products d. bargaining power of union 8. Ans: a, 39. Geometry Multiple Choice Regents Exam Questions www.jmap.org 3 13 Which line is parallel to the line whose equation is 4x +3y =7 and also passes through the point (−5,2)? |A| = a11.C11 + a12.C12 + a13.C13
or equivalently select column 2
|A| = a12.C12 + a22.C22 + a32.C32
so the determinant of A= EMBED Equation.3
(choose row 2 for example�.) e) none of the above C 17. a) decimal Pages: 1 | 2. B 7. Multiple Choice Version 1 Key 1. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. d) = List of top 50 most frequently asked C Language multiple choice questions and answers pdf download free 1. A ) converts a number to string This page provides all MCQs in the 20000 Civil Engineering area in PDF format. Which of the following is used to see if two elements are equal in MATLAB? B ) fixed point display Given!the!matrix!Aabove! rows = no. Instructions. (Question11)whichofthefollowingisthecorrect valuefortheexpression!!!!!=!"#(!)!! Which of the following will correctly define x, y, and z as symbols? Most Asked Technical Basic CIVIL | Mechanical | CSE | EEE | ECE | IT | Chemical | Medical MBBS Jobs Online Quiz Tests for Freshers Experienced. Question 1 ... What is the term used in Ansoff's matrix for increasing market share with existing products in existing markets? “Please never give up your goals at any time and at any cost. D ) Question 2 The following quizzes are from Matrices, Determinants, their properties & key facts. B ) erase everything in the mfile b) x=154! A square matrix A= [aij] is said to be an lower triangular matrix if aij = 0 for ij. If the order of matrix A is . A ) % c) Matrix polysaccharides of plant cell walls are synthesized in the Golgi apparatus and exported to the cell wall by endocytosis. D ) clear the comment Which is these is not an aspect of a for/while loop: Math 2550 Matrix Algebra Multiple Choice Exam Form A Oct. 27, 2014 Problem 1. _____ is based on the assumption that the future will be just like the past. This is a good thing, but there are circumstances in which biased estimates will work a little bit better. Matrix at TU Dresden. e) none of the above What is the value of ans that is printed when the following code is run: isnumeric(32) a) v(0) A = B = Perform the indicated matrix operation, if possible. Find the inverse of the Matrix: 41 A 32 ªº «» ¬¼ Method 1: Gauss – Jordan method Step1: Set up the given matrix with the identity matrix as the form of 4 1 1 0 3 2 0 1 ªº «» ¬¼ Step 2: Transforming the left Matrix into the identical matrix follow the rules of Row operations. Command C. Control D. Getting others to follow 2. Posted on 4th August 2016 By Naukriadmin Leave a comment. B ) add a line space (enter key) College Math Multiple Choice Questions and Answers (MCQs): Quizzes & Practice Tests with Answer Key (College Math Quick Study Guide & Course Review Book 1) contains course review tests for competitive exams to solve 803 MCQs. Ans: d, 34. The output of Ans: a, 37. Exercises (1)Suppose that L 1 and L 2 are lines in the plane, that the x-intercepts of L 1 and L 2 are 5 and 1, respectively, and that the respective y-intercepts are 5 and 1. c) matrix math d) delayed copy e) licenses Ans: d. 8. let aij be amount good j consumed by individual i
columns1-3:represent goods X, Y& Z
rows 1-2:represent individuals 1 & 2
Matrix of consumption
C = EMBED Equation.3 = EMBED Equation.3
Individual 1 consumes 0 of X, 10 of Y and 5 of Z
Individual 2 consumes 4 of X, 0 of Y and 6 of Z
NOTE
Row Vector is a matrix with only 1 row�: A = [5 4 3] 1 X 3 matrix
Column Vector is a matrix with only 1 column�: A = EMBED Equation.3 3 X 1 matrix
Transposing Matrices
A = EMBED Equation.3 2 X 3 matrix
Then
AT = EMBED Equation.3 3X2 matrix
the transpose of a matrix replaces rows by columns. Answer the following questions and then press 'Submit' to get your score. _ 1. e) all are aspects of loops To print a newline in a fprintf statement, you must use the following escape character: a) \t b) \nl c) \nxt d) \n e) none of the above Ans: d. 9. a) != Problems with hoping AB and BA are equal: • BA may not be well-defined. This Matlab command clears all data and variables stored in memory: a. Multiple Choice This activity contains 15 questions. d) string The 2 2× matrix B represents a reflection in the straight line with equation y x= − . 1) 4x +3y =−26 2) 4x +3y =−14 3) 3x +4y =−7 4) 3x +4y =14 14 In a given triangle, the point of intersection of the three medians is the same as the point of Then, you can check out Excel Matrix Templates available online. _____ is increasing Leadership rapidly: A. 1930. b. C 12. Copyright 2020 , Engineering Interview Questions.com, MATLAB Objective type Questions with Answers. A square matrix Ais said to be triangular if it is an upper or a lower triangular matrix. Ans: a, 15. b) % c) runner For example 2 1 4 0 3 −1 0 0 −2 is an upper triangular matrix. examples with detailed response description, explanation is given and it would be easy to understand. C ) comment(‘ ‘) Individual 2 consumes 4 of X, 0 of Y and 6 of Z. e) none of the above We will be there to motivate you”. تمام سابقہ پیپر جات نوٹس اور حل شدہ پیپرز کیلئے یہاں کلک کریں شکریہ . A 18. Choose the alternative that is the d erivatlve, . We look for an “inverse matrix” A 1 of the same size, such that A 1 times A equals I. 0.50 mi: 1.50 mi: 3.00 mi: 6.50 mi: Matrices and Determinants Multiple Choice Questions (MCQs) Page-1. Example: a matrix with 3 rows and 5 columns can be added to another matrix of 3 rows and 5 columns. Calculate the result of the following matrix multiplication: (for 5 points) u r 6. ... 88 MCQs with answers - Part 1 Multiple Choice Questions in Design and Analysis of Algorithms with Answers 1. Determinant of a Matrix
If A = EMBED Equation.3
Now we can find the determinant��
Multiply elements in any one row or any one column by corresponding co-factors, and sum�.. C ) ??? Which of these is the way to access the first element in a vector named v (assuming there is at You may receive points for partially correct answers. In Matlab, this keyword immediately moves to the next iteration of the loop: a) update b) goto c) continue d) break e) none of the above Ans: c. 10. Ans: c, 7. Multiple choice questions and answers on Matrices and Determinants quiz answers PDF 1 to learn math certificate online course. And the order of B is . If the equations a(y + z) = x, b(z + x) = y and c (x + y) = z, where a ¹ –1, b ¹ – 1, c ¹ –1 admit non-trivial solution, then (1 + … Leadership MCQs Multiple Choice Questions 1. FUNDAMENTALS OF LINEAR ALGEBRA James B. Carrell carrell@math.ubc.ca (July, 2005) Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. B ) cat dog True B. A 10. c) continue Matrices and Determinants Multiple Choice Questions and Answers PDF Download. 1: Y - C = I + G
From eq. 3. The following quizzes are from Matrices, Determinants, their properties & key facts. B ) ; Home » C MCQS » 50 TOP c programming multiple choice questions and answers pdf download. Matrices and Determinants MCQs Sheet 1. Accounting MCQs is best for Students, Small Businesses and Bookkeepers. e) none of the above Ans: b, 12. The origins of Business Policy & Strategic Management can be retraced to _____. 3) A = -54 04 A)- 1 5- 1 5 0 1 4 B)- 1 5 1 5 0 1 4 C) 1 4 1 5 0 - 1 5 D) 0 1 4- 1 5 1 5 3) Decide whether or not the matrices are inverses of each other. e) none of the above A = 2 X 3 matrix. Method 3: Using Cramers Rule
In the example above, where
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
Replace column 1 of A with the elements of vector B
EMBED Equation.3
Calculate the determinant of this as:|A1| = (I + G )(1) � ( �1)( a) = I + G + a
We saw earlier that the determinant of A is
| A | = 1� b
Therefore the solution using Cramers rule is:
EMBED Equation.3
Replace column 2 of A with the elements of vector b
EMBED Equation.3
Calculate the determinant of this as:|A2|=(1)(a) � (I+G)(� b) = a+b(I+G)
We saw earlier that the determinant of A is
| A | = 1� b
Therefore the solution using Cramers rule is:
EMBED Equation.3
(just as we derived using the other 2 methods)
To invert 3 X 3 Matrix��
To find inverse of 3 X 3 matrix, First need to calculate determinant
A = EMBED Equation.3
Corresponding to each aij is a co-factor Cij. a) Write down the matrices A and B. Excel Matrix Templates. Matrices Class 12 […] © 2014-2019 The Matrix.org Foundation CIC | Hosted by UpCloud | LegalUpCloud | Legal 4) -24 4 -4 and 1 2 1 4 1 2 1 4 A) Yes B) No 4) Determine whether the matrix is invertible. � �2 � �2 yV YG Q6 yV YG YG oH � -T h � � iU �2 - Pw4�R�� d+ [? " c) // as=num2str(aa) Pages: 1 | 2. Which of the following is not a pre-defined variable in Matlab. b) Matrix Laboratory (2) into eq. To hide the internal implementation of an object we use … d) condition 3. Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 4 Determinants. Matrices and determinants quiz questions and answers PDF, rectangular matrix quiz, column matrix quiz, multiplication of matrix quiz, homogeneous linear equations quiz, symmetric matrix quizzes for colleges offering online degree programs. A matrix is a visual presentation of your business data using rows and columns. c) syms x, y, z Instructions. Transposing Matrices. But it could not be added to a matrix with 3 rows and 4 columns (the columns don't match in size) Negative. Use these in-depth, customizable worksheets to help students master matrices, a vital area of mathematics for electrical circuits, quantum mechanics, programming, and more. c) \nxt 2.5. d) Nothing ��ࡱ� > �� M O ���� L � ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ U@ �� �) bjbj���� � �� �� �! Learn accounting principles, financial statements, debits & credits and more. b) 0 MCQS MIDTERM EXAMINATION ... 22u matrix, the area of the parallelogram determined by the columns of A is det A adj A Question No: 22 ( Marks: 1 ) - Please choose one . <3.8mmol/L B. 12. What will the value of a be equal to if this What does Matlab stand for? Unit III Quiz Question Sampler 2.086/2.090 Fall 2012. Chapter 11: Multiple choice questions. Which of the following quantities is considered a vector? a) 1 b) 2 c) 3 d) 4 2. Matrix multiplication not commutative In general, AB = BA. If I want to save a formatted string to memory, but don’t want to print it out, which What symbol precedes all comments in Matlab? To join one or more strings into a single string is known as command should I use? PAGE
PAGE 15
B 8. Replies. row of a matrix to another row (or adds a multiple of one equation to another) is a row operation of type III. D ) & b) \nl Ans: b, 32. b) clear (e.g., A is 2 x 3 matrix, B is 3 x 5 matrix) (e.g., A is 2 x 3 matrix, B is 3 x 2 matrix) C ) concatenates numbers and strings Question 1. What a matrix mostly does is to multiply a vector x. Ans: b, 6. �T yV �V 0 �V �T � v[ }E � v[ iU � � � � � � v[ � iU Q6 Q6 YG Q6 Q6 Q6 Q6 Q6 �V �V � � �$ d+ CG � � d+ MATRICES
Course Manual
Topic 2.5�: Vector and Matrix Notation
Topic 12.1
Jacques (3rd Edition):
Chapter 7.1- 7.2
A Vector: list of numbers arranged in a row or column
e.g. a) update CLINICAL CHEMISTRY MCQs A. CARBOHYDRATES. b) initialization A ) add a space between any two characters A ) single character display Students can solve NCERT Class 12 Maths Matrices MCQs Pdf with Answers to know their preparation level. A ) clear the command window c) v A ) concatenation d) break Characters in Matlab are represented in their value in memory. b) == Ans: b, 13. If vector = [1 2 3 4; 11 24 92 100; 345 65 90 1]. Academia.edu is a platform for academics to share research papers. aij � bij = eij
EMBED Equation.3
Multiplying Matrices
To multiply A and B,
No. In Matlab, this keyword immediately moves to the next iteration of the loop: a) update b) goto c) continue d) break e) none of the above Ans: c. 10. consumption of 10 units X and 6 units of Y gives a consumption vector (X,Y) of (10,6) ( (6,10)
A Matrix: a two-dimensional array of numbers arranged in rows and columns
e.g. Ans: c, 36. Write a matrix that shows the monthly profit for each pet shop. Ans: a. 4. 2 Robert Beezer xSSLE Setting these expressions for yequal, we have the equation 5 8x= 2x 3, which quickly leads to x= 3 Substituting for xin the rst equation, we have y= 5 x= 5 8 3 = 7 3. Column Vector. Determinants Class 12 […] B 15. b)sprintf L M W Y d w x � g i k l � � � � � � � � � � � ) B 11. d) v(: , 0) b) ASCII < 3.0mmol/L C. <2.8mmol/L D. <5.0mmol/L _____2. The determinant of a square matrix A is nonzero if and only if the equation Ax = 0 has a unique solution. Find answers and solutions to the questions at the bottom of the page. C ) disp(‘Question 2’) Thus, the solution is x= 8 3, y= 7 3. A 14. is B ) display(‘Question 2’) Created by T. Madas Created by T. Madas Question 4 (**) The 2 2× matrix A represents a rotation by 90 ° anticlockwise about the origin O. Select row 1�. Find the values of xand y given the following equation:; First, I'll simplify the left-hand side a bit by adding entry-wise: d) yes This means that b is an unbiased estimate of β . These Strategic Management Multiple Choice Questions can be used for quizzes, internal exams, entrance exams, skill tests or aptitude tests. C 5. 1. c) 32 These Matrices Objective Questions with Answers are important for competitive exams UGC NET, GATE, IBPS Specialist Recruitment Test. Read Multiple Choice Questions and answers. D ) save the existing mfile Ans: d, 4. c) i 1. Ans: b, 35. A. When used in the fprintf command, the \n is used to b) goto Row Vector. e) none of the above B 13. Here we have given Strategic Management MCQ with Answers. Matrices and Determinants Multiple Choice Questions and Answers (MCQs), matrices and determinants quiz answers PDF 1, college math tests to study online certificate courses. Their product is the identity matrix—which does nothing to a vector, so A 1Ax D x. C = = Individual 1 consumes 0 of X, 10 of Y and 5 of Z. �����Ƹ�ݮ�ݡ����ݓ݂r��g�\�\�g� h@X� CJ. Admin 19 December 2018 at 01:10. And the order of B is . C ) clean the desktop d) echo b) inf a) \t It is helpful for all kind of Civil Engineering examinations. least one element in the vector)? a) 1 Dec 02,2020 - Linear Algebra MCQ - 1 | 20 Questions MCQ Test has questions of Computer Science Engineering (CSE) preparation. d) delayed copy "College Math MCQ" with answers helps with fundamental concepts for self-assessment with theoretical, analytical, and distance learning. To print a newline in a fprintf statement, you must use the following escape character: cat=[‘cat’ as], A ) cat2 Ans: a, 38. (2) and solve for C:
EMBED Equation.3
Method 2
Now solve the same problem using matrix algebra:
Rewrite (1) and (2) with endogenous variables, C and Y, on left hand side
From eq. The output of the last line is b) scalars Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 3 Matrices. Ans: e, 14. View matrices.doc from MATH AP at Dulaney High. 1. c) matrix math C ) place a number into the comment code is entered into MATLAB >>[a b] = size (vector)? The clc command is used to Students can solve NCERT Class 12 Maths Matrices MCQs Pdf with Answers to know their preparation level. The matrix notation will allow the proof of two very helpful facts: * E b = β . a) update Inverse Matrices 81 2.5 Inverse Matrices Suppose A is a square matrix. The Revenue and Expenses for two pet shops for a 2-month period are shown below. • Even if AB and BA are both defined, BA may not be the same size. Ans: d, 8. Find A + B. d) 4 a) vectors Answer the following questions and then press 'Submit' to get your score. 5) 6 1 3 4 A) Yes B) No 5) 6) 8 5 -8 7 2 -7 … Ans: b, 11. B ) cat 2 A= EMBED Equation.3 then AT = EMBED Equation.3
Adding and Subtracting Matrices
Matrices must have same number of rows and columns, m X n
Just add (subtract) the corresponding elements�..
A + B + C = D i.e. d) The direction of cellulose microfibril growth is determined by the orientation of arrays of microtubules lying just below the plasma membrane. Algebra 2 Matrices Review Multiple Choice Identify the choice that best completes the statement or answers the question. D 4. c) disp D ) default number display Ans: b, 2. You can extend the rows and columns of your data in an excel sheet without repeating the numbers. Where appropriate, write down intermediate calculations. ID: A unique ID number used to identify the traceability item in the requirements traceability matrix. B ) joining In recent years, the need for supporting digital tools for team collaboration has increased. Find answers and solutions to the questions at the bottom of the page. Matrix is a free and open, secure, decentralized protocol for real-time communication, also known by the name of one of its clients, Element. Hypoglycemia comes about for various reasons and clinical symptoms usually occur at blood glucose concentrations: A. Mathematics → Matrices & Determinants MCQs. Question 1 What is the term for organisational development through a formally designed organisational structure? It only takes a minute to sign up. Reply. Then . All MCQs and Past Papers Online MCQs Quiz Tests are here. I and G are exogenous. Below are Strategic Management MCQ with solutions. Test and improve your knowledge of Algebra II: Matrices and Determinants with fun multiple choice exams you can take online with Study.com Cramer’s rule leads easily to a general formula for the inverse of n x n matrix A In Matlab, this keyword immediately moves to the next iteration of the loop: Select row 1�. a) Product development b) Market penetration cat=[‘cat’ ‘dog’] D 19. A 2. A matrix is basically an organized box (or “array”) of numbers (or other expressions). Quiz on Matrix Multiplication Solutions to Exercises Solutions to Quizzes The full range of these packages and some instructions, should they be required, can be obtained from our web page Mathematics Support Materials. aa=2 a) fprintf e) none of the above d) deallocate For download All Past Papers. Learn rectangular matrix MCQs, "Matrices and Determinants" quiz questions and answers for admission and merit scholarships test. The augmented matrix is in row-echelon form and represents a system of linear equations. Strategy B. c) 1 The num2str command d) \n d\' dx' fhf . a) pi _____1. aij + bij + cij = dij
EMBED Equation.3
A - B = E i.e. C31 (Chris Black) Find all solutions to the linear system: Store documents online and access them from any computer. c) isequal Find the inverse of the matrix, if it exists. Undefined function or variable ‘as’ c) Mathworks Co-factor Cij = determinant of 2X2 matrix obtained by deleting row i and column j of A, prefixed by + or � according to following pattern�
EMBED Equation.3
e.g. Ans: a, 40. In this chapter, we will typically assume that our matrices contain only numbers. (Last Updated On: February 5, 2020) This is the Multiple Choice Questions Part 1 of the Series in Advanced Engineering Math topic in Engineering Mathematics. Example Here is a matrix of size 2 3 (“2 by 3”), because it has 2 rows and 3 columns: 10 2 015 The matrix consists of 6 entries or elements. a) 1 2 3 4 a) sym (x, y, z) To add a comment to the mfile, the MATLAB command is Find the volume of the parallelepiped determined by vectors |A| = a11.C11 + a12.C12 = ad � bc
Select column 2
|A| = a12.C12 + a22.C22 = b(-c)+da
MATRIX INVERSION
Square matrix: no. • Even if AB and BA are both defined and of the same size, they still may not be equal. For Quiz 3 (on Unit III) you will need a calculator (for arithmetic operations and standard func 50 TOP c programming multiple choice questions and answers pdf download. 1. 2: -bY + C = a
Now write this in matrix notation: EMBED Equation.3
EMBED Equation.3
or A.X = B
We can solve for the endogenous variables X, by calculating the inverse of the A matrix and multiplying by B:
Since AX=B ( X=A-1B
To invert the 2 X 2 A matrix, recall the steps from earlier in the lecture
If A = EMBED Equation.3 , then A �1 = EMBED Equation.3
In this case, where EMBED Equation.3
the determinant of A is :
|A| = 1.1 � [� 1.� b] = 1 � b
Cofactor Matrix: EMBED Equation.3
Transpose Cofactor Matrix: EMBED Equation.3
The inverse is�:
EMBED Equation.3
EMBED Equation.3 so X=A-1B
where EMBED Equation.3 and EMBED Equation.3
EMBED Equation.3
Thus, multiplying A-1B gives,
EMBED Equation.3
These are the solutions for the endogenous variables, C and Y, just as we derived using method 1. B 20. 1. D 16. 1911. c. 1879 Temperature: Distance: Mass: Displacement: Find the distance a hiker walks if he travels 3.50 mi north, and then turns around and walks 3.00 mi south. D ) concatenates strings C23 is co-factor associated with a23, in row 2 and column 3
so delete row 2 and column 3 to give a 2X2 matrix
EMBED Equation.3
co-factor C23 is � determinant of 2X2 matrix (negative sign in position a23)
C23 = � EMBED Equation.3 = � (a11.a32 � a12.a31)
e.g find all co-factors of matrix
A = EMBED Equation.3
C11 = (delete row 1 column 1, compute determinant of remaining 2X2 matrix, position a11 associated with +)
EMBED Equation.3 and + EMBED Equation.3 = +[3.3 � (7.1)] = 2
C12 = (delete row 1 column 2, compute determinant of remaining 2X2 matrix, position a21 associated with -)
EMBED Equation.3 and � EMBED Equation.3 = � [4.3 � (7.2)] = +2
Other co-factors compute as
C13 = + EMBED Equation.3 = +[4.1 � (3.6)] = -2
C21 = � EMBED Equation.3 = � [4.3 � (1.1)] = �11
C22= + EMBED Equation.3 = +[2.3 � (1.2)] = 4
C23= � EMBED Equation.3 = � [2.1 � (4.2)] = 6
C31 = + EMBED Equation.3 = +[4.7 � (1.3)] = 25
C32= � EMBED Equation.3 = � [2.7 � (1.4)] = -10
C33= + EMBED Equation.3 = +[2.3 � (4.4)] = -10
Co-factor Matrix = EMBED Equation.3 Now we can find the determinant��
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