Exercise 9.B.6

Answers

Proof. Define $T \in L (ℝ^{2})$ by

T (x, y) = (x + y, y) .

Then $span ((1, 0))$ is invariant under $T$ , however, its orthogonal complement, namely $span ((0, 1))$ , is not, because

T (0, 1) = (1, 1) \notin span ((0, 1)) .

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celiopassos

2017-10-06 00:00