Please give an explanation for your answer I want to understand thank you also please answer all Determine if each statement below is true or false.1. Suppose AB = AC. Then B = C.2. (A+ B)" = A" + B"%3D3. A(BC) = (AC)B4. (AB)- = A-!B-15. Suppose AB = AC and A is invertible. Then B = C.6. If A is an invertible n x n matrix, then Ax = b is consistent for all b in R".7. If the columns of an n x n matrix A span R", then the columns of A are linearlyindependent.8. If the equation Ax = b has more than one solution for some b in R", then the columnsof A span R".9. If A is an n x n matrix and the equation Ax = 0 has a nontrivial solution, then A hasfewer than n pivots.10. Every square triangular matrix is invertible.11. Every line in R" is a subspace of R".12. Every line through the origin in R" is a subspace of R".13. The dimension of Nul(A) is the number of variables in the equation Ax = 0.14. The dimension of Col(A) is the number of pivot columns of A.15. Col(A) is the set of solutions to Ax = b.

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Answered: Determine if each statement below is…

Determine if each statement below is true or false. 1. Suppose AB AC. Then B = C. 2. (A+ B)" = A" + B" %3D 3. A(BC) = (AC)B

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 32E

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Question

Please give an explanation for your answer I want to understand thank you also please answer all

Determine if each statement below is true or false.
1. Suppose AB = AC. Then B = C.
2. (A+ B)" = A" + B"
%3D
3. A(BC) = (AC)B
4. (AB)- = A-!B-1
5. Suppose AB = AC and A is invertible. Then B = C.
6. If A is an invertible n x n matrix, then Ax = b is consistent for all b in R".
7. If the columns of an n x n matrix A span R", then the columns of A are linearly
independent.
8. If the equation Ax = b has more than one solution for some b in R", then the columns
of A span R".
9. If A is an n x n matrix and the equation Ax = 0 has a nontrivial solution, then A has
fewer than n pivots.
10. Every square triangular matrix is invertible.
11. Every line in R" is a subspace of R".
12. Every line through the origin in R" is a subspace of R".
13. The dimension of Nul(A) is the number of variables in the equation Ax = 0.
14. The dimension of Col(A) is the number of pivot columns of A.
15. Col(A) is the set of solutions to Ax = b.

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