Which of the following subsets of R are subspaces of RX2 A. The 3 x 3 matrices in reduced row-echelon form B. The 3 x 3 matrices of rank 2 C. The 3 x 3 matrices whose entries are all integers. D. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) E. The 3 x 3 matrices with all zeros in the third row F. The 3 x 3 matrices A such that the vector 4. is in the kernel of A 6. 口口

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Which of the following subsets of R* are subspaces of R*?
A. The 3 x 3 matrices in reduced row-echelon form
B. The 3 x 3 matrices of rank 2
C. The 3 x 3 matrices whose entries are all integers
D. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries)
E. The 3 x 3 matrices with all zeros in the third row
F. The 3 x 3 matrices A such that the vector
4.
is in the kernel of A
6.
口口
Transcribed Image Text:Which of the following subsets of R* are subspaces of R*? A. The 3 x 3 matrices in reduced row-echelon form B. The 3 x 3 matrices of rank 2 C. The 3 x 3 matrices whose entries are all integers D. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) E. The 3 x 3 matrices with all zeros in the third row F. The 3 x 3 matrices A such that the vector 4. is in the kernel of A 6. 口口
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