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**Unformatted text preview: **Homework Set 2 for MAS 4105
Due Friday, January 27
1. Use Gaussian elimination to ﬁnd all solutions to the following system
of equations.
− x1 − x2 − x3 + x4 = 2
x1 + x2 + x3 + x4 = 0
x1
− 2x 3
=2
2. In each case determine whether y ∈ Span(S ).
(a) V = R3 , S = {(1, 2, 3), (2, 3, 4)}, y = (1, 1, 0) (b) V = P2 (F ), S = {1 + x, −1 + x2 }, (c) V = M2×2 (F ), S=
y= 01
20 , y = 2 + x − x2 −1 −1
11 , 0 −1
00 , 12
3 −1 The following problems are strongly recommended, but should not be
turned in:
3.4: 2acegi
1.5: 1, 2abcdef, 4, 5, 7, 9, 11, 17
1.6: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13 ...

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