Determine if the set is a basis for R 3
. Justify your answer ⎣
⎡
​ 0
0
−4
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​ , ⎣
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​ 1
2
8
​ ⎦
⎤
​ , ⎣
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​ 2
4
4
​ ⎦
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​ Is the given set a basis for R 3
? 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 R n. . B. 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 R n
. C. 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 R n
. D. 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 R n. .