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Determine if the set is a basis for R³. Justify your answer. 0 1 Love 2 4 2 -3 6 3 Is the given set a basis for R³? A. No, because these three vectors form the columns of a 3x3 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". B. Yes, because these three vectors form the columns of an invertible 3 x 3 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 Rn. C. No, because these three vectors form the columns of an invertible 3x3 matrix. By the invertible matrix theore 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 D. Yes, because these three vectors form the columns of a 3x3 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 linear independent set, and the columns of A span Rn.

Determine if the set is a basis for R³. Justify your answer. 0 1 Love 2 4 2 -3 6 3 Is the given set a basis for R³? A. No, because these three vectors form the columns of a 3x3 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". B. Yes, because these three vectors form the columns of an invertible 3 x 3 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 Rn. C. No, because these three vectors form the columns of an invertible 3x3 matrix. By the invertible matrix theore 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 D. Yes, because these three vectors form the columns of a 3x3 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 linear independent set, and the columns of A span Rn.

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 R³. Justify your answer. 0 - 3 1 6 2 3 Is the given set a basis for R³? O A. No, because these three vectors form the columns of a 3×3 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 Rn. B. Yes, because these three vectors form the columns of an invertible 3×3 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 Rº. O C. No, because these three vectors form the columns of an invertible 3×3 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 Rn. D. Yes, because these three vectors form the columns of a 3×3 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 Rn.
Transcribed Image Text:Determine if the set is a basis for R³. Justify your answer. 0 - 3 1 6 2 3 Is the given set a basis for R³? O A. No, because these three vectors form the columns of a 3×3 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 Rn. B. Yes, because these three vectors form the columns of an invertible 3×3 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 Rº. O C. No, because these three vectors form the columns of an invertible 3×3 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 Rn. D. Yes, because these three vectors form the columns of a 3×3 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 Rn.
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