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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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