Advanced Linear Algebra : Transformations, Basis and Eigenvalues
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(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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