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Exercise 2.6.5

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Assume that $p (t) = a + bx$ . We have $\int_{0}^{1} (a + bt) dt = a + \frac{b}{2}$ and $\int_{0}^{2} (a + bt) dt = 2 a + 2 b$ . So we may returen the representation such that

a + bx = (a + \frac{b}{2}) (2 - 2 x) + (2 a + 2 b) (- \frac{1}{2} + x) .

We may check that the set ${2 - 2 x, - \frac{1}{2} + x}$ is a basis and hence the desired set. By Theorem 2.24 ${f_{1}, f_{2}, f_{3}}$ is a basis for $V^{∗}$ .

jephianlin

2011-06-27 00:00

Exercise 2.6.5

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