The trace of an nxn matrix A. written trace(A). is defined to be the sum trace(A) = a₁ + a₂2+ + ann. ª22 Prove that, for any n x n matrices A and B and scalar c. the following statements are true: A (a) trace(A + B)= trace(A) + trace(B). (b) trace(cA) = c -trace(A). (c) trace(A)= trace(A).
The trace of an nxn matrix A. written trace(A). is defined to be the sum trace(A) = a₁ + a₂2+ + ann. ª22 Prove that, for any n x n matrices A and B and scalar c. the following statements are true: A (a) trace(A + B)= trace(A) + trace(B). (b) trace(cA) = c -trace(A). (c) trace(A)= trace(A).
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:82 The trace of an n×n matrix A. written trace(A), is
defined to be the sum
trace(A) = a₁ + a₂ + + ann.
Prove that, for any n x n matrices A and B and scalar c.
the following statements are true: A
(a) trace(A + B) = trace(A) + trace(B).
(b) trace(cA)=c-trace(A).
(c) trace(A¹) = trace(A).
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