Which of the following subsets of R³×3 are subspaces of R³×3? x3 A. The 3 x 3 matrices of determinant 1 B. The 3 x 3 matrices with determinant 0 C. The 3 x 3 matrices with all zeros in the first row
Which of the following subsets of R³×3 are subspaces of R³×3? x3 A. The 3 x 3 matrices of determinant 1 B. The 3 x 3 matrices with determinant 0 C. The 3 x 3 matrices with all zeros in the first row
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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Transcribed Image Text:Which of the following subsets of R³×3
are subspaces of R³×3?
A. The 3 x 3 matrices of determinant 1
B. The 3 x 3 matrices with determinant 0
C. The 3 x 3 matrices with all zeros in the first
row
D. The 3 x 3 matrices with trace 0 (the trace
of a matrix is the sum of its diagonal entries)
E. The invertible 3 x 3 matrices
F. The 3 x 3 matrices A such that
8
A
¹0-0
=
7
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