Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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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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