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\textbf{Math 228: Intro to Lin Alg \& Diff Eqns}
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\textbf{Quiz 4}\quad \textsl{February 21, 2002}
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1. Determine which of the following sets $S$ are subspaces of the given
vector space $V$. Be sure to justify your statements.

a) $S = \{ (1+x, 2+2x) \,|\, x\in\R \}$, $V = \R^2$

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b) Let $A$ be an $m\times n$ matrix. $S = \{ \x\in \R^n\,|\, A\x = \0 \}$,
$V = \R^n$

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c) Let $f,g\in C[a,b]$. $S = \{ t f + s g\, | \, t,s\in \R \}$, $V =
C[a,b]$

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2. Let $S = \{ (0,1,1,1), (1,1,1,0), (1,0,0,1) \}$. Determine whether $S$ is
linearly dependent or linearly independent.


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