r there is a b in R" such that the oquation Ax = bis inconsistent, then the transformation x Ax is not one-to-one. hoose the correct answer below. OA. The statement is false. According to the Invertible Matrix Theorem, if there is a b in R" such that the equation Ax=bis inconsistent, then the linear transformation x Ax maps R" onto R". OB. The statement is true. According to the Invertible Matrix Theorem, if there is a b in R" such that the equation Axbis inconsistent, then equation Axb does not have at least one solution for each bin R" and this makes A not Invertible

r there is a b in R" such that the oquation Ax = bis inconsistent, then the transformation x Ax is not one-to-one. hoose the correct answer below. OA. The statement is false. According to the Invertible Matrix Theorem, if there is a b in R" such that the equation Ax=bis inconsistent, then the linear transformation x Ax maps R" onto R". OB. The statement is true. According to the Invertible Matrix Theorem, if there is a b in R" such that the equation Axbis inconsistent, then equation Axb does not have at least one solution for each bin R" and this makes A not Invertible

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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Question

For this exercise assume that the mathces are
1om Statement 1', then "statement 2" Mark an implication as True if the truth of "statement2 aways folloWS whenever "statement
The statement in this exerdise
an imp
1 happens to be truve. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer.
It there is a b in R" such that the equation Ax = b is inconsistent, then the transformation x Ax is not one-to-one.
Choose the correct answer below.
O A. The statement is false. According to the Invertible Matrix Theorem, if there is a b in R such that the equation Ax b is inconsistent, then the linear transformation xAx maps R" onto R".
O B. The statoment in true. According to the Invertible Matrix Theorem, if there is a bin R" such that the equation Ax bis inconsistent, then equation Ax b does not have at least one solution for each b in R" and this makes A not
invertible.
OC. The statement is false. According to the Invertible Matrix Theorem, if there is a b in R" such that the equation Axb is inconsistent, then equation Axb has at least one solution for each b in R" and this makes A invertble.
OD. The statement is true. According to the Invertible Matrix Theorem, If there is a b in R" such that the equation Ax b is inconsistent, then matrix A is invertible.

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