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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

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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.2: Matrix Algebra
Problem 37EQ
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Suppose A is an n × 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 A has fewer than n pivots. O has a nontrivial solution, then 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 the columns of A span R". O has the trivial solution, then Yes e. If the linear transformation T(x) = Ax is onto, then it is also one-to-one. Yes Note: saying Ax that Ax = 0 necessarily has only the trivial solution. 0 has the trivial solution does not mean
Transcribed Image Text:Suppose A is an n × 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 A has fewer than n pivots. O has a nontrivial solution, then 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 the columns of A span R". O has the trivial solution, then Yes e. If the linear transformation T(x) = Ax is onto, then it is also one-to-one. Yes Note: saying Ax that Ax = 0 necessarily has only the trivial solution. 0 has the trivial solution does not mean
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