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Let trace: Rnxn à R be a function defined as trace(A): = Sum[i=1 à n] aii, for all A ∈ Rnxn Write a proof that if β ∈ R, and A,B are arbitrary matrices ∈ Rnxn, then trace (βA + B) = β*trace(A) + trace(B)

Let trace: Rnxn à R be a function defined as trace(A): = Sum[i=1 à n] aii, for all A ∈ Rnxn Write a proof that if β ∈ R, and A,B are arbitrary matrices ∈ Rnxn, then trace (βA + B) = β*trace(A) + trace(B)

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 trace: Rnxn à R be a function defined as

trace(A): = Sum[i=1 à n] aii, for all A ∈ Rnxn

Write a proof that if β ∈ R, and A,B are arbitrary matrices ∈ Rnxn, then

trace (βA + B) = β*trace(A) + trace(B)

Expert Solution
Step 1

Given : Trace of A=∑ aiii=1n

To Prove : traceβA+B=β trace A+traceB

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