Which of the following subsets of R³×3 are subspaces of R³×³? A. The 3 x 3 matrices of rank 2 B. The 3 × 3 matrices whose entries are all greater than or equal to 0 C. The 3 x 3 matrices with all zeros in the second row D. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) E. The 3 × 3 matrices in reduced row-echelon form F. The 3 x 3 matrices A such that the vector 2 is in the kernel of A 8
Which of the following subsets of R³×3 are subspaces of R³×³? A. The 3 x 3 matrices of rank 2 B. The 3 × 3 matrices whose entries are all greater than or equal to 0 C. The 3 x 3 matrices with all zeros in the second row D. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) E. The 3 × 3 matrices in reduced row-echelon form F. The 3 x 3 matrices A such that the vector 2 is in the kernel of A 8
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...
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