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無年度 - 主題課程_向量空間：基底和維度#108872
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題組內容
Find the dimensions of the following subspaces of R
4
.
(c) (5%) All vectors of the form (a, b, c, d), where a= b = c = d.
其他申論題
(10%) If the polynomial function f(x) = ax4 + bx3 + cx2 + dx +e satisfies f(-2)= 150 f(-1) = 16 f(0) = 2 f(1) = 18 f(2) = 166, then a,b, c, d,e are____，____，____，____，____ respectively.
#466845
(a) (5%) All vectors of the form (a, b, c, 0).
#466846
(b) (5%) All vectors of the form (a, b, c, d), where d= a + b and c = a - b.
#466847
(a) (4 points) Choose a subset of which forms a basis for V.
#466849
(b) (4 points) Extend this basis to a basis for R3.
#466850
a) (5%) Find an orthonormal basis for the subspace of R3 spanned by .
#466851
b) (5%) Extend the basis you found in part(a) to an orthonormal basis for R3.
#466852
a. (2 points) Prove that V is a subspace of C[-1, 1].
#466853
b. (5 points) Prove that B = is a basis of V.
#466854
(5 points) Prove that B'= is a basis of V.
#466855
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