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Show that U is a subspace of M3×3(R). Find a basis for U. You need to justify (or it must be clear from your work) that your list of vectors is indeed a basis for U.

Show that U is a subspace of M3×3(R). Find a basis for U. You need to justify (or it must be clear from your work) that your list of vectors is indeed a basis for U.

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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Let M3x3(R) be the vector space of 3x3 real matrices and let U = {M e M3x3 (R): the sum of the diagonal elements of M is 0} (a) Show that U is a subspace of M3x3(R). (b) Find a basis for U. You need to justify (or it must be clear from your work) that your list of vectors is indeed a basis for U.
Transcribed Image Text:Let M3x3(R) be the vector space of 3x3 real matrices and let U = {M e M3x3 (R): the sum of the diagonal elements of M is 0} (a) Show that U is a subspace of M3x3(R). (b) Find a basis for U. You need to justify (or it must be clear from your work) that your list of vectors is indeed a basis for U.
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