4. (AB)-1 = A-B-1 5. Suppose AB AC and A is invertible. Then B = C. %3D 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.
4. (AB)-1 = A-B-1 5. Suppose AB AC and A is invertible. Then B = C. %3D 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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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Please answer 13 and 14 this is my last ask
Transcribed Image Text:4. (AB)-1 = 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.
%3D
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