23 4) Let A be the following matrix: 45 67 (i) Compute A A. (ii) Now, for a general matrix A, (not a specific example --- do not use specific entries and do not choose a specific size) prove that the entry in the T row and i¹ column of AA must be the sum of the squares of the row of th A. T (iii) Prove that for a general matrix A, the trace of the product AA is the sum of the squares of the entries of A.
23 4) Let A be the following matrix: 45 67 (i) Compute A A. (ii) Now, for a general matrix A, (not a specific example --- do not use specific entries and do not choose a specific size) prove that the entry in the T row and i¹ column of AA must be the sum of the squares of the row of th A. T (iii) Prove that for a general matrix A, the trace of the product AA is the sum of the squares of the entries of 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:2 3
4) Let A be the following matrix: 4 5
(i) Compute A AT.
6 7
(ii) Now, for a general matrix A, (not a specific example do not use
specific entries and do not choose a specific size) prove that the entry in the
th
th
T
th
row and i column of AA must be the sum of the squares of the i row of
A.
T
(iii) Prove that for a general matrix A, the trace of the product AA is the
sum of the squares of the entries of A.
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