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Unformatted text preview: (b) Is the union V ∪ W necessarily a subspace of < 3 ? Explain your answer. 5. Consider the linear system x + yz = 2 x + 2 y + z = 3 x + y + ( k 25) z = k where k is an arbitrary constant. For which choice(s) of k does this system have a unique solution ? For which choice(s) of k does the system have inﬁnitely many solutions ? For which choice(s) of k is the system inconsistent ? 1 6. Does the subset W = { ( x,y )  x,y, ∈ < , and x,y ≥ 0 or x,y ≤ } i.e., the union of the ﬁrst and third quadrants of the ( x,y )plane < 2 , constitute a subspace (over the real numbers) of the ( x,y )plane ? (i) True (ii) False 2...
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 Fall '07
 UNKNOWN
 Linear Algebra, Set Theory, column space

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