If 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 x Ax maps R" onto R O B. 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 equation Ax =b does not have at least one solution for each b in R" and this makes A not invertible. O C. 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 equation Ax =b has at least one solution for each b in R" and this makes A invertible. O D. 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.

If 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 x Ax maps R" onto R O B. 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 equation Ax =b does not have at least one solution for each b in R" and this makes A not invertible. O C. 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 equation Ax =b has at least one solution for each b in R" and this makes A invertible. O D. 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.

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 matrices are all nxn. The statement in this exercise is an Implication of the form "If statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement
1" happens to be true. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer.
If 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 x Ax maps R" onto R".
O B. The statement is true. According to the lInvertible Matrix Theorem, if there is a b in R" such that the equation Ax = b is inconsistent, then equation Ax = b does not have at least one solution for each b in R" and this makes A not
invertible
O C. The statement
false. According to the Invertible Matrix Theorem, if there is ab in R" such that the equation Ax =b is inconsistent, then equation Ax = b has at least one solution for each b in R" and this makes A invertible
O D. 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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