20F Quiz 2

20F Quiz 2 - Name: PID: TA: Sec. No: Sec. Time: Math 20F...

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: Name: PID: TA: Sec. No: Sec. Time: Math 20F Quiz 2 April 18, 2008 1. Consider the vectors 1 v1 = −1 , 4 3 v2 = −5 , 7 −1 v3 = 5 . h For what value(s) of h are the vectors {v1 , v2 , v3 } linearly dependent? Solution: h = 6 2 −2 0 1 , y1 = −1 , , e2 = y2 = 0 . 2. Let e1 = 1 0 3 4 2 3 Let T : R → R be the linear transformation defined by T (e1 ) = y1 and T (e2 ) = y2 . (a) Find the matrix A which represents T in the sense that T (x) = Ax for all x ∈ R2 . 2 −1 Solution: A = 3 −2 0 4 3 2 (b) Find the images of Solution: x1 x2 x1 x1 under T . 2 2 −2 3 3 = −3 , = −1 0 2 2 17 3 4 2x1 − 2x2 2 −2 3 −x1 . 0 = = −1 2 3x1 + 4x2 3 4 T T and ...
View Full Document

This note was uploaded on 04/29/2008 for the course MATH 20F taught by Professor Buss during the Spring '03 term at UCSD.

Ask a homework question - tutors are online