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7. Consider the 2 x 2 matrix A over C with det(A) = 1. %3D (i) Find the inverse of A. (ii) Let v be a normalized vector in C2. Is the vector Av normalized? (iii) Let 1 E = -1 0 Calculate AEAT. (iv) Let B be a 2 x 2 matrix over C with det(B) = 1. Find the 4 x 4 matrix (A® B)(E ® E)(A® B)". %3D

7. Consider the 2 x 2 matrix A over C with det(A) = 1. %3D (i) Find the inverse of A. (ii) Let v be a normalized vector in C2. Is the vector Av normalized? (iii) Let 1 E = -1 0 Calculate AEAT. (iv) Let B be a 2 x 2 matrix over C with det(B) = 1. Find the 4 x 4 matrix (A® B)(E ® E)(A® B)". %3D

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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7. Consider the 2 x 2 matrix A over C with det(A) = 1. %3D (i) Find the inverse of A. (ii) Let v be a normalized vector in C?. Is the vector Av normalized? (iii) Let - (오 ) 1 E = -1 0 Calculate AEAT. (iv) Let B be a 2 x 2 matrix over C with det(B) = 1. Find the 4 x 4 matrix (A® B)(E® E)(A ® B)". %3D
Transcribed Image Text:7. Consider the 2 x 2 matrix A over C with det(A) = 1. %3D (i) Find the inverse of A. (ii) Let v be a normalized vector in C?. Is the vector Av normalized? (iii) Let - (오 ) 1 E = -1 0 Calculate AEAT. (iv) Let B be a 2 x 2 matrix over C with det(B) = 1. Find the 4 x 4 matrix (A® B)(E® E)(A ® B)". %3D
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