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 x 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 x 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 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...

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