Question

Let
v1 = (1, 0, −1)

v2 = (0, 2, 2)

v3 = (−3, 4, 7)

and let W = Span{v1, v2, v3}.

1. Show that v3 is a linear combination c1v1 + c2v2 of v1 and v2 by finding
the constants c1 and c2.

2. Show that W = Span{v1, v2}.

3. Show that v1 and v2 are linearly independent.

4. What is the dimension of W?

Answer 1

a-3c=0
2b+4c=0
-a+2b+7c=0

3v1 - 2v2 + v3 = 0
v3 = 2v2 - 3v1

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