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20F Quiz 2

# 20F Quiz 2 - Name PID TA Sec No Sec Time Math 20F Quiz 2 1...

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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 ...
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