Question: Q. {u1, u2} and {v1, v2} be ordered bases for R 2 , where u1 = ( 1 ,1 )T , u2 = ( 1

Q. {u1, u2} and {v1, v2} be ordered bases for R 2 , where

u1 = ( 1 ,1 )T , u2 = ( 1 1 )T , v1 = ( 2 ,1 )T , v2 =( 1 0 )T

(T represents transpose)

Let L be the linear transformation defined by L(x) = (x1, x2) T and let B be the matrix representing L with respect to {u1, u2}.

(a) Find the transition matrix S corresponding to the change of basis from {u1, u2} to {v1, v2}.

(b) Find the matrix A representing L with respect to {v1, v2} by computing SBS^1 .

(c) Verify that

L(v1) = a11v1 + a21v2

L(v2) = a12v1 + a22v2

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