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 "statement 1" is true. Justify your answer. IHA' is not invertible, then A is not invertible. Choose the correct answer below. O A. The statement is false. By the Invertible Matrix Theorem, if A' is not invertible, then all statements in the theorem are true, including A is invertible. Therefore, A is invertible. O B. The statement is true. By the Invertible Matrix Theorem, if A' is not invertible, then there is an nxn matrix C such that CA = I. This means that A must not be invertible. O C. The statement is false. By the Invertible Matrix Theorem, if A' is not invertible, then there is not an nxn matrix C such that CA = I. Therefore, A is invertible. O D. The statement is true. By the Invertible Matrix Theorem, if A' is not invertible, then all statements in the theorem are false, including Ais invertible. Therefore, A is not 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 "statement 1" is true. Justify your answer. IHA' is not invertible, then A is not invertible. Choose the correct answer below. O A. The statement is false. By the Invertible Matrix Theorem, if A' is not invertible, then all statements in the theorem are true, including A is invertible. Therefore, A is invertible. O B. The statement is true. By the Invertible Matrix Theorem, if A' is not invertible, then there is an nxn matrix C such that CA = I. This means that A must not be invertible. O C. The statement is false. By the Invertible Matrix Theorem, if A' is not invertible, then there is not an nxn matrix C such that CA = I. Therefore, A is invertible. O D. The statement is true. By the Invertible Matrix Theorem, if A' is not invertible, then all statements in the theorem are false, including Ais invertible. Therefore, A is 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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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

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 A' is not invertible, then A is not invertible.
Choose the correct answer below.
O A. The statement is false. By the Invertible Matrix Theorem, if A' is not invertible, then all statements in the theorem are true, including A is invertible. Therefore, A is invertible.
O B. The statement is true. By the Invertible Matrix Theorem, if A' is not invertible, then there is an nxn matrix C such that CA =I. This means that A must not be invertible.
O C. The statement is false. By the Invertible Matrix Theorem, if A' is not invertible, then there is not an nxn matrix C such that CA = I. Therefore, A is invertible.
O D. The statement is true. By the Invertible Matrix Theorem, if A' is not invertible, then all statements in the theorem are false, including A is invertible. Therefore, A is not invertible.

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