Which of the following subsets of R³×3 are subspaces of R³×³? A. The non-invertible 3 x 3 matrices B. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) C. The invertible 3 x 3 matrices

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 7TFE
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Which of the following subsets of R³×3 are subspaces of R³×32
A. The non-invertible 3 x 3 matrices
B. The 3 × 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries)
C. The invertible 3 × 3 matrices
D. The 3 x 3 matrices A such that the vector
E. The 3 x 3 matrices of rank 2
F. The 3 x
5
3 is in the kernel of A
6
matrices with all zeros in the first row
Transcribed Image Text:Which of the following subsets of R³×3 are subspaces of R³×32 A. The non-invertible 3 x 3 matrices B. The 3 × 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) C. The invertible 3 × 3 matrices D. The 3 x 3 matrices A such that the vector E. The 3 x 3 matrices of rank 2 F. The 3 x 5 3 is in the kernel of A 6 matrices with all zeros in the first row
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