Question

Which of the following subsets of R^3x3 (the vector space of 3 x 3 matrices) are subspaces of R^3x3? A. The 3 x 3 matrices with all zeros in the second row B. The 3 x 3 matrices A such that the vector (7 8 6)^T is in the kernel of A C. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) D. The 3 x 3 matrices of rank 2 E. The 3 x 3 matrices whose entries are all integers F. The 3 x 3 matrices in reduced row-echelon form

          Which of the following subsets of R^3x3 (the vector space of 3 x 3 matrices) are subspaces of R^3x3?

A. The 3 x 3 matrices with all zeros in the second row
B. The 3 x 3 matrices A such that the vector (7 8 6)^T is in the kernel of A
C. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries)
D. The 3 x 3 matrices of rank 2
E. The 3 x 3 matrices whose entries are all integers
F. The 3 x 3 matrices in reduced row-echelon form

Which of the following subsets of R^3x3 (the vector space of 3 x 3 matrices) are subspaces of R^3x3?

A. The 3 x 3 matrices with all zeros in the second row
B. The 3 x 3 matrices A such that the vector (7 8 6)^T is in the kernel of A
C. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries)
D. The 3 x 3 matrices of rank 2
E. The 3 x 3 matrices whose entries are all integers
F. The 3 x 3 matrices in reduced row-echelon form

Added by Aurora W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/18/2023

Step 1

The set of 3 matrices with all zeros in the second row is a subspace of R3x3. To show this, we need to check that it satisfies the three conditions for a subset to be a subspace: - It contains the zero vector: the zero matrix has all zeros in the second row, Show more…

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Which of the following subsets of R3x3 (the vector space of 3x3 matrices) are subspaces of R3x3? A. The 3x3 matrices with all zeros in the second row. B. The 3x3 matrices such that the vector in the kernel of A. C. The 3x3 matrices with trace (the sum of its diagonal entries) matrices of rank. D. The 3x3 matrices whose entries are all integers. E. The 3x3 matrices in reduced row-echelon form.