6. Theorem A matrix A is nonsingular if and only if det(A)#0. Which of the following matrices are nonsingular? If the matrix is invertible (nonsingular), then find its inverse. 3 -5] a) -2 -1 3 2 2 -4 b) 1 5 0 1 2 c) 1 2 0 4 2 4 6 -2 3 7 -2 1 3 4

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter2: Matrices
Section2.3: The Inverse Of A Matrix
Problem 79E: Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A....
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show your solution, answer 6 and 7

6. Theorem A matrix A is nonsingular if and only if det(A)# 0. Which of the
following matrices are nonsingular? If the matrix is ivertible (nonsingular), then find
its inverse.
2 2 4
b) |1 5 2
3 7 -2
4
3 -5]
0 1 27
a)
-2 -1
3
c) | 1 2 0
4
6 -2
1 3 4
7. Solve the given linear system by Cramer's Rule.
2x+3y+ 7z=2
а) -2х
х-у+ z3-1
b) 2х+ у-3z38
x-2y+3z=-5
- 4z=0
X+ 2 y+ 4z= 0
Transcribed Image Text:6. Theorem A matrix A is nonsingular if and only if det(A)# 0. Which of the following matrices are nonsingular? If the matrix is ivertible (nonsingular), then find its inverse. 2 2 4 b) |1 5 2 3 7 -2 4 3 -5] 0 1 27 a) -2 -1 3 c) | 1 2 0 4 6 -2 1 3 4 7. Solve the given linear system by Cramer's Rule. 2x+3y+ 7z=2 а) -2х х-у+ z3-1 b) 2х+ у-3z38 x-2y+3z=-5 - 4z=0 X+ 2 y+ 4z= 0
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