Quiz4-Solutions

# Quiz4-Solutions - x 2 2 x 2 + x 4 x 2-x 4 = x 1 1 + x 2 2 2...

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Name:. ......................................................................................... Math 331 - Quiz 4 - Solutions Thursday, October 6 1. Assume that T is a linear transformation. Find the standard matrix of T if T : R 2 7→ R 4 , T ( e 1 ) = (3 , 1 , 3 , 1) and T ( e 2 ) = ( - 5 , 2 , 0 , 0) where e 1 = (1 , 0) and e 2 = (0 , 1). Solution: The standard matrix for T is the matrix with columns T ( e 1 ) and T ( e 2 ) so the standard matrix is 3 - 5 1 2 3 0 1 0 2. Let T ( x 1 ,x 2 ,x 3 ,x 4 ) = ( x 1 + 2 x 2 , 0 , 2 x 2 + x 4 ,x 2 - x 4 ). Show that T is a linear transformation by ﬁnding a matrix that implements the mapping. Solution: T x 1 x 2 x 3 x 4 = x 1 + 2
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Unformatted text preview: x 2 2 x 2 + x 4 x 2-x 4 = x 1 1 + x 2 2 2 1 + x 3 + x 4 1-1 = 1 2 0 0 0 0 0 2 0 1 0 1 0-1 x 1 x 2 x 3 x 4 So T ( x ) = A x where A = 1 2 0 0 0 0 0 2 0 1 0 1 0-1 So T is a linear transform with standard matrix A ....
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## This document was uploaded on 04/02/2012.

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