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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. OA. 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™. OB. 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. OC. The statement is true. According to the Invertible Matrix Theorem, if there is a b in Rº 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 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.

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. OA. 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™. OB. 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. OC. The statement is true. According to the Invertible Matrix Theorem, if there is a b in Rº 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 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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 32E
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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. B. 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 C. The statement is true. According to the Invertible Matrix Theorem, if there is a b in R inconsistent, then equation Ax=b does not have at least one solution for each b in R D. The statement is true. According to the Invertible Matrix Theorem, if there is a b in R inconsistent, then matrix A is invertible. such that the equation Ax = b is and this makes A not invertible. such that the equation Ax=b is
Transcribed Image Text: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. B. 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 C. The statement is true. According to the Invertible Matrix Theorem, if there is a b in R inconsistent, then equation Ax=b does not have at least one solution for each b in R D. The statement is true. According to the Invertible Matrix Theorem, if there is a b in R inconsistent, then matrix A is invertible. such that the equation Ax = b is and this makes A not invertible. such that the equation Ax=b is
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