Exercise 6.B.3

Answers

Proof. Applying the Gram-Schmidt Procedure to the given basis, we get the following basis

(1, 0, 0), \frac{1}{\sqrt{2}} (0, 1, 1), \frac{1}{\sqrt{2}} (0, - 1, 1) .

As in the proof of 6.37, we see that the matrix of $T$ with respect to this basis is upper triangular.

Exercise 5

Applying the Gram-Schmidt Procedure, we get the following basis

1, 2 \sqrt{3} (x - \frac{1}{2}), 6 \sqrt{5} (x^{2} - x + \frac{1}{6}) .

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celiopassos

2017-10-06 00:00