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Determine if the set of all 2 x 2 matrices where tr(A) = 0 is a subspace of the vector space, M2x2, with the standard operations of addition and scalar multiplication. Verify your answer with a brief explanation. 2.

Determine if the set of all 2 x 2 matrices where tr(A) = 0 is a subspace of the vector space, M2x2, with the standard operations of addition and scalar multiplication. Verify your answer with a brief explanation. 2.

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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Determine if the set of all 2 x 2 matrices where tr(A) = 0 is a subspace of the vector space, M2x2, with the standard operations of addition and scalar multiplication. Verify your answer with a brief explanation. 2.
Transcribed Image Text:Determine if the set of all 2 x 2 matrices where tr(A) = 0 is a subspace of the vector space, M2x2, with the standard operations of addition and scalar multiplication. Verify your answer with a brief explanation. 2.
Expert Solution
Step 1

We know the definition of subspaces,

A non empty subset S of a vector space V is said to be subspace of V if it satisfies the following property,

If A, B ∈ S and λ be any scalar then A+λB∈S.

We have given that, V is a vector space of 2×2 matrices with standard operations of addition and scalar multiplication.

Also, S=A∈M2×2 / trA=0 

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