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Given: A e M2x2(R). a. Given T: M2x2 (R) → M2x2 (R) as T(M) = AM, prove that rank (T) = 2rank(A). b. Given U: M2xn (R) → M2xn(R) as U(M) = AM, express more generally the rank of U in %3D terms of n and the rank of A. Please only answer this question if you are sure it is correct. Thank you so much!

Given: A e M2x2(R). a. Given T: M2x2 (R) → M2x2 (R) as T(M) = AM, prove that rank (T) = 2rank(A). b. Given U: M2xn (R) → M2xn(R) as U(M) = AM, express more generally the rank of U in %3D terms of n and the rank of A. Please only answer this question if you are sure it is correct. Thank you so much!

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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Given: A e M2x2(R). a. Given T: M2x2(R) → M2x2 (R) as T(M) = AM, prove that rank (T) = 2rank(A). b. Given U: M2xn(R) → M2xn (R) as U(M) = AM, express more generally the rank of U in terms of n and the rank of A. Please only answer this question if you are sure it is correct. Thank you so much!
Transcribed Image Text:Given: A e M2x2(R). a. Given T: M2x2(R) → M2x2 (R) as T(M) = AM, prove that rank (T) = 2rank(A). b. Given U: M2xn(R) → M2xn (R) as U(M) = AM, express more generally the rank of U in terms of n and the rank of A. Please only answer this question if you are sure it is correct. Thank you so much!
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