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(a) Consider the matrix 4 0 4 7 -5 1 A = 3 -1 2 1 -6 0 (i) Compute the determinant of A. (ii) Using your answer to part (i), explain whether A is invertible or not. (Do not attempt to compute the in- verse.)

(a) Consider the matrix 4 0 4 7 -5 1 A = 3 -1 2 1 -6 0 (i) Compute the determinant of A. (ii) Using your answer to part (i), explain whether A is invertible or not. (Do not attempt to compute the in- verse.)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.1: The Determinants Of A Matrix
Problem 43E: True or False ? a The determinant of a 22 matrix A is a21a12a11a22. b The determinant of a matrix of...
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(a) Consider the matrix 7 -5 1 4 0 0 4 A = 3 -1 2 0 1 -6 0 (i) Compute the determinant of A. (ii) Using your answer to part (i), explain whether A is invertible or not. (Do not attempt to compute the in- verse.) 5. Com- (b) Suppose that B is a square matrix with det(B) pute the following: (i) det(B³); (ii) det(B-!); (iii) det(B"). (c) Suppose that C is a 4x4 matrix with det(C) = 3. Compute the determinants of the following matrices: (i) the matrix obtained by swapping the first and second rows of C; (ii) the matrix obtained by multiplying the fourth row of С bу —6; |
Transcribed Image Text:(a) Consider the matrix 7 -5 1 4 0 0 4 A = 3 -1 2 0 1 -6 0 (i) Compute the determinant of A. (ii) Using your answer to part (i), explain whether A is invertible or not. (Do not attempt to compute the in- verse.) 5. Com- (b) Suppose that B is a square matrix with det(B) pute the following: (i) det(B³); (ii) det(B-!); (iii) det(B"). (c) Suppose that C is a 4x4 matrix with det(C) = 3. Compute the determinants of the following matrices: (i) the matrix obtained by swapping the first and second rows of C; (ii) the matrix obtained by multiplying the fourth row of С bу —6; |
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