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Advanced Linear Algebra : Transformations, Basis and Eigenvalues

(See attached file for complete problem description)

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Let T: IR^3 IR^3 T(x,y,z) = (y+z, x+z, y+x)

B1 = standard basis of IR^3 and B2 the basis

B2 = {u1= (1,1,1), u2 = (1, -1,0), u3 = (1,1,-2)}

- Find A= [ T ] , B = [ T ]
B1 B2

- Prove that A is similar to B

Hint: Find P = [ I ] , Q = [ I ] where I(v) = v
B2, B1 B1,B2

- Show that Q = p^-1 and A= PBp^-1

- Find the eigenvalues of T
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(See attached file for complete problem description)

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Solution Summary

Transformations, Basis and Eigenvalues are investigated. The solution is detailed and well presented.

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