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Linear Algebra

Exercise 2.6.3

Answers

1.

We may find out that for all vector

(x, y, z) \in ℝ^{3}

we can express it as

(x, y, z) = (x - \frac{y}{2}) (1, 0, 1) + \frac{y}{2} (1, 2, 1) + (z - x) (0, 0, 1) .

So we can write

{\begin{matrix} f_{1} (x, y, z) = x - \frac{y}{2}; \\ f_{2} (x, y, z) = \frac{y}{2}; \\ f_{3} (x, y, z) = z - x . \end{matrix}

2.

This is much easier and we have that

{\begin{matrix} f_{1} (a_{0} + a_{1} x + a_{2} x^{2}) = a_{0}; \\ f_{2} (a_{0} + a_{1} x + a_{2} x^{2}) = a_{1}; \\ f_{3} (a_{0} + a_{1} x + a_{2} x^{2}) = a_{2} . \end{matrix}

jephianlin

2011-06-27 00:00

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