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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 Spring '03
 BUSS
 Linear Algebra, Derivative, Vectors, Math 20F

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