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9. Let z = x + iy with x, y ER and thus z = x – iy. Consider the maps - A(z.9), 1++ (6), i(?). I -y x + iy + (i) Calculate z? and A²(x, y). Discuss. (ii) Find the eigenvalues and normalized eigenvectors of A(x, y). (iii) Calculate A(x,y) ® A(x, y) and find the eigenvalues and normalized eigen- vectors.

9. Let z = x + iy with x, y ER and thus z = x – iy. Consider the maps - A(z.9), 1++ (6), i(?). I -y x + iy + (i) Calculate z? and A²(x, y). Discuss. (ii) Find the eigenvalues and normalized eigenvectors of A(x, y). (iii) Calculate A(x,y) ® A(x, y) and find the eigenvalues and normalized eigen- vectors.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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9. Let z = x + iy with x, Y E R and thus z = x – iy. Consider the maps iy + (; ?) - atr.v), 1++ (;). i+(!) = A(x, y), 1++ ()- x + iy + (i) Calculate z? and A2(x,y). Discuss. (ii) Find the eigenvalues and normalized eigenvectors of A(x, y). (iii) Calculate A(x,y) ® A(x,y) and find the eigenvalues and normalized eigen- vectors.
Transcribed Image Text:9. Let z = x + iy with x, Y E R and thus z = x – iy. Consider the maps iy + (; ?) - atr.v), 1++ (;). i+(!) = A(x, y), 1++ ()- x + iy + (i) Calculate z? and A2(x,y). Discuss. (ii) Find the eigenvalues and normalized eigenvectors of A(x, y). (iii) Calculate A(x,y) ® A(x,y) and find the eigenvalues and normalized eigen- vectors.
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