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
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.
Transcribed Image Text: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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