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Linear Algebra

Exercise 5.4.2

Answers

1.

Yes. For every

a x^{2} + bx + c \in W

, we have

T (a x^{2} + bx + c) = 2 ax + b \in W .

2.

Yes. For every

a x^{2} + bx + c \in W

, we have

T (a x^{2} + bx + c) = 2 a x^{2} + bx \in W .

3.

Yes. For every

(t, t, t) \in W

, we have

T (t, t, t) = (3 t, 3 t, 3 t) \in W .

4.

Yes. For every

at + b \in W

, we have

T (at + b) = (\frac{a}{2} + b) t \in W .

5.

No. For

(\begin{matrix} 1 & 0 \\ 0 & 2 \end{matrix}) \in W

, we have

T (A) = (\begin{matrix} 0 & 2 \\ 1 & 0 \end{matrix}) \notin W .

jephianlin

2011-06-27 00:00

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