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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 the columns of A are linearly independent, then the columns of A span R. Choose the correct answer below. O A. The statement is true. By the Invertible Matrix Theorem, if the columns of A are linearly dependent, then the columns of A must span R. O B. The statement is false. By the Invertible Matrix Theorem, if the columns of A are linearly dependent, then the columns of A must span R. OC. The statement is false. By the Invertible Matrix Theorem, if the columns of A are linearly independent, then the columns of A do not span R. O D. The statement is true. By the Invertible Matrix Theorem, if the columns of A are linearly independent, then the columns of A must span R.

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 the columns of A are linearly independent, then the columns of A span R. Choose the correct answer below. O A. The statement is true. By the Invertible Matrix Theorem, if the columns of A are linearly dependent, then the columns of A must span R. O B. The statement is false. By the Invertible Matrix Theorem, if the columns of A are linearly dependent, then the columns of A must span R. OC. The statement is false. By the Invertible Matrix Theorem, if the columns of A are linearly independent, then the columns of A do not span R. O D. The statement is true. By the Invertible Matrix Theorem, if the columns of A are linearly independent, then the columns of A must span R.

Advanced Engineering Mathematics
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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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 the columns of A are linearly independent, then the columns of A span R". Choose the correct answer below. O A. The statement is true. By the Invertible Matrix Theorem, if the columns of A are linearly dependent, then the columns of A must span R. O B. The statement is false. By the Invertible Matrix Theorem, if the columns of A are linearly dependent, then the columns of A must span R. O C. The statement is false. By the Invertible Matrix Theorem, if the columns of A are linearly independent, then the columns of A do not span R. D. The statement is true. By the Invertible Matrix Theorem, if the columns of A are linearly independent, then the columns of A must span R.
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 the columns of A are linearly independent, then the columns of A span R". Choose the correct answer below. O A. The statement is true. By the Invertible Matrix Theorem, if the columns of A are linearly dependent, then the columns of A must span R. O B. The statement is false. By the Invertible Matrix Theorem, if the columns of A are linearly dependent, then the columns of A must span R. O C. The statement is false. By the Invertible Matrix Theorem, if the columns of A are linearly independent, then the columns of A do not span R. D. The statement is true. By the Invertible Matrix Theorem, if the columns of A are linearly independent, then the columns of A must span R.
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