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Determine if the set is a basis for R. Justify your answer. - 12 Is the given set a basis for R2? O A. No, because these vectors form the columns of an invertible 2x2 matrix. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R". O B. Yes, because these vectors form the columns of an invertible 2x2 matrix. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R". OC. No, because these vectors form the columns of a 2x2 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R". O D. Yes, because these vectors form the columns of a 2x2 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R".

Determine if the set is a basis for R. Justify your answer. - 12 Is the given set a basis for R2? O A. No, because these vectors form the columns of an invertible 2x2 matrix. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R". O B. Yes, because these vectors form the columns of an invertible 2x2 matrix. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R". OC. No, because these vectors form the columns of a 2x2 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R". O D. Yes, because these vectors form the columns of a 2x2 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A 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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Determine if the set is a basis for R. Justify your answer. 4 - 12 - 3 9. Is the given set a basis for R? O A. No, because these vectors form the columns of an invertible 2x2 matrix. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R". B. Yes, because these vectors form the columns of an invertible 2x2 matrix. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R". C. No, because these vectors form the columns of a 2x2 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R". D. Yes, because these vectors form the columns of a 2x2 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R".
Transcribed Image Text:Determine if the set is a basis for R. Justify your answer. 4 - 12 - 3 9. Is the given set a basis for R? O A. No, because these vectors form the columns of an invertible 2x2 matrix. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R". B. Yes, because these vectors form the columns of an invertible 2x2 matrix. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R". C. No, because these vectors form the columns of a 2x2 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R". D. Yes, because these vectors form the columns of a 2x2 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R".
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