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題組內容

2. (8 points) The following vectors span a subspace Y of R³, but not a basis for V, Answer the following questions.

(b) (4 points) Extend this basis to a basis for R³.

其他申論題

(a) (5%) All vectors of the form (a, b, c, 0).

(b) (5%) All vectors of the form (a, b, c, d), where d= a + b and c = a - b.

(c) (5%) All vectors of the form (a, b, c, d), where a= b = c = d.

(a) (4 points) Choose a subset of which forms a basis for V.

a) (5%) Find an orthonormal basis for the subspace of R3 spanned by .

b) (5%) Extend the basis you found in part(a) to an orthonormal basis for R3.

a. (2 points) Prove that V is a subspace of C[-1, 1].

b. (5 points) Prove that B = is a basis of V.

(5 points) Prove that B'= is a basis of V.

甲、論文部分(七十分)：請以藍、黑色鋼筆或原子筆在申論試卷上直式作答，於本試題上作答者，不予計分。服務的人生觀

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