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Determine if the set is a basis for R3. Justify your answer. 886 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". OB. 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 linearly independent set, and the columns of A span R". OC. Yes, because these three vectors form the columns of an invertible 3x3 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". OD. No, because these three vectors form the columns of an invertible 3x3 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.

Determine if the set is a basis for R3. Justify your answer. 886 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". OB. 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 linearly independent set, and the columns of A span R". OC. Yes, because these three vectors form the columns of an invertible 3x3 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". OD. No, because these three vectors form the columns of an invertible 3x3 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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 45E
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Determine if the set is a basis for R3. Justify your answer. 886 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". OB. 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 linearly independent set, and the columns of A span R". OC. Yes, because these three vectors form the columns of an invertible 3x3 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". OD. No, because these three vectors form the columns of an invertible 3x3 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.
Transcribed Image Text:Determine if the set is a basis for R3. Justify your answer. 886 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". OB. 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 linearly independent set, and the columns of A span R". OC. Yes, because these three vectors form the columns of an invertible 3x3 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". OD. No, because these three vectors form the columns of an invertible 3x3 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.
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