solutions3bd

solutions3bd - Math 33a/2, Quiz 3bd, November 1, 2007 Name:...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 33a/2, Quiz 3bd, November 1, 2007 Name: Suppose v1 = UCLA ID: 3 2 and v2 = . Note that {v1 , v2 } = B are a basis for R2 . Let 6 5 T : R2 R2 be the linear transformation such that T (v1 ) = v1 + v2 and T (v2 ) = 2v1 - 3v2 . 1. Compute the matrix of T with respect to the basis B. 2. Compute the standard matrix of T . 1 and 1 2 1 2 T (v2 ) B = . Hence the matrix B of T relative to the basis B is simply . -3 1 -3 5 -2 3 2 1 The change-of-basis matrix S is simply , and we compute S -1 = (3)(5)-(2)(6) -6 3 6 5 5 -2 1 = 3 . Hence the standard matrix A of T is given by -6 3 1 3 2 3 -6 1 2 A = SBS -1 = ( ) 6 5 1 -3 3 -2 5 1 5 0 3 -6 = ( ) 11 -3 3 -2 5 1 15 -30 = 3 39 -81 5 -10 = . 13 -27 Solution. Since T (v1 ) = v1 + v2 and T (v2 ) = 2v1 - 3v2 , we have T (v1 ) B = 1 ...
View Full Document

This note was uploaded on 04/02/2008 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.

Ask a homework question - tutors are online