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(a) Which element of 1 0 4. 2 3 1 3 B = 3 A = 3 7 8 4 3 7. 8. 4 is represented by a32? (b) Is A a square matrix? (c) Find the transpose of matrix A. (d) Does A = B? Solution a) a32 represents the element in row 3 and column 2 of matrix A-that is, a3, = 8.

(a) Which element of 1 0 4. 2 3 1 3 B = 3 A = 3 7 8 4 3 7. 8. 4 is represented by a32? (b) Is A a square matrix? (c) Find the transpose of matrix A. (d) Does A = B? Solution a) a32 represents the element in row 3 and column 2 of matrix A-that is, a3, = 8.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
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why is a32 = 8?
Lo o We define two matrices to be equal if they are of the same order and if each entry in one equals the corresponding entry in the other. When the columns and rows of matrix A are interchanged to create a matrix B and vice versa, we say that A and B are transposes of each other and write AT = B and B" = A. We will see valuable uses for transposes of matrices in Chapter 4, "Inequalities and Linear Programming." E 2 Matrices (a) Which element of 3 1 3 A = 4 B = 3 4. 8 3 8. 4. is represented by a32? (b) Is A a square matrix? (c) Find the transpose of matrix A. (d) Does A = B? Solution (a) a32 represents the element in row 3 and column 2 of matrix A-that is, a3, = 8. (b) Yes, it is a 3 X 3 (square) matrix. (c) 1 3 7. AT 0. 4. 8. 3 3 (d) No, a33 # b33. 1. (a) Do matrices A andB have the same order? 3 1. 4. A = 4. 6. and B = 8. 3. 6. 6. (b) Does matrix A equal matrix B? (c) Does BT = A? ion If two matrices have the same number of rows and columns, we can add the m 49
Transcribed Image Text:Lo o We define two matrices to be equal if they are of the same order and if each entry in one equals the corresponding entry in the other. When the columns and rows of matrix A are interchanged to create a matrix B and vice versa, we say that A and B are transposes of each other and write AT = B and B" = A. We will see valuable uses for transposes of matrices in Chapter 4, "Inequalities and Linear Programming." E 2 Matrices (a) Which element of 3 1 3 A = 4 B = 3 4. 8 3 8. 4. is represented by a32? (b) Is A a square matrix? (c) Find the transpose of matrix A. (d) Does A = B? Solution (a) a32 represents the element in row 3 and column 2 of matrix A-that is, a3, = 8. (b) Yes, it is a 3 X 3 (square) matrix. (c) 1 3 7. AT 0. 4. 8. 3 3 (d) No, a33 # b33. 1. (a) Do matrices A andB have the same order? 3 1. 4. A = 4. 6. and B = 8. 3. 6. 6. (b) Does matrix A equal matrix B? (c) Does BT = A? ion If two matrices have the same number of rows and columns, we can add the m 49
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