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無年度 - 主題課程_線性映射：判斷線性#107849
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題組內容
Let I' be a linear operator on R
3
such that
,
,
(b)Find
其他申論題
Let .Show that is linear combination of A and I2.
#462097
Suppose that T: R2→R3 is a linear transformation such that and Determine for any in R2.
#462098
Let T be a linear operator on R3 such that T, Please find the standard matrix of T.
#462099
(a) Find .
#462100
Let Y be the vector space of 2x2 mattices with real entries, and P3 the vector space of real polynomials of dogree 3 or less. Detine the linear transformation T: V → P3 by == 2a+(6-d)t-(a+c)x2+(a+6-c-d)x3. Find the rank and nullity of T.
#462102
(a). Prove that if ker T= {0}; then T is one-to-one.(7 pts)
#462103
(b). Suppose T is one-to-one and {u1,... ,uk} is a linearly independent set of vectors in U. Prove that [T(u1),....,T(uk)] is a linearly independent set of vectors in V.(7 pts)
#462104
(c). Define UP(t)(a polynomil of degree 2 and its standard form is P(t) = a0+ a1t + a2t2),V R3, and T(U) = Find U such that the image under T of Uis [11, 1, -1]T. (7 pts)
#462105
(a) (5%) Find a vector u = (ux, uy, uz) such that T(u) - u and.
#462106
(b) (5%) Is T : R3 → R3 one-to-one and onto? Why or why not?
#462107
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