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You only have 5 attempts for this problem. Suppose A is an n x n matrix. Select "yes" if the statement is always true, "no" if the statement is always false, and "maybe" if the statement is sometimes true and sometimes false. a. If the equation Ax = 0 has a nontrivial solution, then A has fewer than n pivots. Yes b. If -A is not invertible, then A is also not invertible. Yes c. If the linear transformation T(x) = Ax is one-to-one, then the columns of A form a linearly dependent set. No d. If the equation Ax = 0 has the trivial solution, then the columns of A span R". Yes e. If the linear transformation T(x) = Ax is onto, then it is also one-to-one. Yes Note: saying Ax = 0 has the trivial solution does not mean that Ax = 0 necessarily has only the trivial solution.

You only have 5 attempts for this problem. Suppose A is an n x n matrix. Select "yes" if the statement is always true, "no" if the statement is always false, and "maybe" if the statement is sometimes true and sometimes false. a. If the equation Ax = 0 has a nontrivial solution, then A has fewer than n pivots. Yes b. If -A is not invertible, then A is also not invertible. Yes c. If the linear transformation T(x) = Ax is one-to-one, then the columns of A form a linearly dependent set. No d. If the equation Ax = 0 has the trivial solution, then the columns of A span R". Yes e. If the linear transformation T(x) = Ax is onto, then it is also one-to-one. Yes Note: saying Ax = 0 has the trivial solution does not mean that Ax = 0 necessarily has only the trivial solution.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 4CC
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my answers arent correct. Please help!

You only have 5 attempts for this problem. Suppose A is an n x n matrix. Select "yes" if the statement is always true, "no" if the statement is always false, and "maybe" if the statement is sometimes true and sometimes false. a. If the equation Ax = 0 has a nontrivial solution, then A has fewer than n pivots. Yes b. If -A is not invertible, then A is also not invertible. Yes c. If the linear transformation T(x)= Ax is one-to-one, then the columns of A form a linearly dependent set. No d. If the equation Ax = 0 has the trivial solution, then the columns of A span R". Yes e. If the linear transformation T(x) = Ax is onto, then it is also one-to-one. Yes Note: saying Ax = 0 has the trivial solution does not mean that Ax = 0 necessarily has only the trivial solution.
Transcribed Image Text:You only have 5 attempts for this problem. Suppose A is an n x n matrix. Select "yes" if the statement is always true, "no" if the statement is always false, and "maybe" if the statement is sometimes true and sometimes false. a. If the equation Ax = 0 has a nontrivial solution, then A has fewer than n pivots. Yes b. If -A is not invertible, then A is also not invertible. Yes c. If the linear transformation T(x)= Ax is one-to-one, then the columns of A form a linearly dependent set. No d. If the equation Ax = 0 has the trivial solution, then the columns of A span R". Yes e. If the linear transformation T(x) = Ax is onto, then it is also one-to-one. Yes Note: saying Ax = 0 has the trivial solution does not mean that Ax = 0 necessarily has only the trivial solution.
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