Page 202 - 35Linear Algebra

202 Subspaces and Spanning Sets

9.3 Review Problems

Reading Problems 1 , 2
Webwork: Subspaces 3, 4, 5, 6
Spans 7, 8

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3
3
2
1. Determine if x − x ∈ span{x , 2x + x , x + x }.
2. Let U and W be subspaces of V . Are:
(a) U ∪ W

(b) U ∩ W

3
also subspaces? Explain why or why not. Draw examples in R .

Hint

3
3
3. Let L : R → R where
L(x, y, z) = (x + 2y + z, 2x + y + z, 0) .

3
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Find kerL, imL and the eigenspaces R , R . Your answers should be
3
−1
3
subsets of R . Express them using span notation.

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