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Q.3 (12 pts) Consider the matrices U = 1 2 34 and V = in the a 2 7 a vector space M22, the vector space of all 2 x 2 matrices with real entries with the standard inner product < u, v >= tr(UTV) for given matrices u = U and v=V. For what value(s) of a are the matrices orthoganal?

Q.3 (12 pts) Consider the matrices U = 1 2 34 and V = in the a 2 7 a vector space M22, the vector space of all 2 x 2 matrices with real entries with the standard inner product < u, v >= tr(UTV) for given matrices u = U and v=V. For what value(s) of a are the matrices orthoganal?

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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Q.3 (12 pts) Consider the matrices U = 1 2 34 and V = in the a 2 7 a vector space M22, the vector space of all 2 x 2 matrices with real entries with the standard inner product < u, v >= tr(UTV) for given matrices u = U_and v=V. For what value(s) of a are the matrices orthoganal?
Transcribed Image Text:Q.3 (12 pts) Consider the matrices U = 1 2 34 and V = in the a 2 7 a vector space M22, the vector space of all 2 x 2 matrices with real entries with the standard inner product < u, v >= tr(UTV) for given matrices u = U_and v=V. For what value(s) of a are the matrices orthoganal?
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