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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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(10%) If the polynomial function f(x) = ax
4
+ bx
3
+ cx
2
+ 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.
其他申論題
(b) Those p(x) for which p(0) = 1.(3%)
#466841
(c) Those p(x) for which a+b =c+ d.(4%)
#466842
(10 pts) Find the coordinate vector of the polynomial x3 -4x2 + 3x +7 relative to the ordered basis B' = ((x-2)3, (x-2)2, (x-2), 1) ofthe vector space P3.
#466843
(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
(c) (5%) All vectors of the form (a, b, c, d), where a= b = c = d.
#466848
(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
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