Determine if the set is a basis for R°. Justify your answer. 6 -4 1 1 - 4 Is the given set a basis for R3? O A. No, because these two vectors are linearly dependent. O B. Yes, because these vectors form the columns of an invertible 3 x3 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". O C. No, because these vectors form a matrix with only 2 pivot columns. Therefore, these vectors form a basis for a two-dimensional subspace of R3. O D. Yes, because these two vectors are linearly independent.
Determine if the set is a basis for R°. Justify your answer. 6 -4 1 1 - 4 Is the given set a basis for R3? O A. No, because these two vectors are linearly dependent. O B. Yes, because these vectors form the columns of an invertible 3 x3 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". O C. No, because these vectors form a matrix with only 2 pivot columns. Therefore, these vectors form a basis for a two-dimensional subspace of R3. O D. Yes, because these two vectors are linearly independent.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 66E
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