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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
Consider the vector space of polynomials of the form p(x) = ax
3
+ bx
2
+ cx+d.
Are the following subspaces? Explain briefy.
(b) Those p(x) for which p(0) = 1.(3%)
其他申論題
Find the basis of the vector space V= (5%)
#466837
(a)p1,p2,p3是否線性獨立。(10%)
#466838
(b)寫出span{p1,p2,p3)(10%)
#466839
(a) Those p(x) for which p(1) =0.(3 %)
#466840
(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
(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
(c) (5%) All vectors of the form (a, b, c, d), where a= b = c = d.
#466848
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