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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Question:** Which of the following subsets of \(\mathbb{R}^{3 \times 3}\) are subspaces of \(\mathbb{R}^{3 \times 3}\)? - **A.** The \(3 \times 3\) matrices of rank 2 - **B.** The \(3 \times 3\) matrices whose entries are all greater than or equal to 0 - **C.** The \(3 \times 3\) matrices with all zeros in the second row - **D.** The \(3 \times 3\) matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) - **E.** The \(3 \times 3\) matrices in reduced row-echelon form **F.** The \(3 \times 3\) matrices \(A\) such that the vector \(\begin{pmatrix} 6 \\ 2 \\ 8 \end{pmatrix}\) is in the kernel of \(A\)
Transcribed Image Text:**Question:** Which of the following subsets of \(\mathbb{R}^{3 \times 3}\) are subspaces of \(\mathbb{R}^{3 \times 3}\)? - **A.** The \(3 \times 3\) matrices of rank 2 - **B.** The \(3 \times 3\) matrices whose entries are all greater than or equal to 0 - **C.** The \(3 \times 3\) matrices with all zeros in the second row - **D.** The \(3 \times 3\) matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) - **E.** The \(3 \times 3\) matrices in reduced row-echelon form **F.** The \(3 \times 3\) matrices \(A\) such that the vector \(\begin{pmatrix} 6 \\ 2 \\ 8 \end{pmatrix}\) is in the kernel of \(A\)
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