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轉學考-線性代數
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92年 - 92 淡江大學 轉學考 線性代數#56121
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5. Let T : P
2
→ R
2
be deflned by T(a+bx+cx
2
) = (a-b,c+a)
and B={1, x,x
2
}，D={(1,-1)，(0，1)}. Find the matrix of T corresponding to the ordered bases B and D. (10 points)
其他申論題
2. LetT: R3 → R2 be a linear transformation and T(l，0，0)=(l，-2)，T(l,l,0)=(l,3), T(0,0，l)=(2，-1). Find T(x，y，z). (10 points)
#213186
(a) Find general solutions of AX=0. (10 points)
#213187
(b) Find Rank(A). (5points)
#213188
【已刪除】4. Let P=. Show that P is invertible and find p-1 .(10 points)
#213189
6. Suppose that {x, y} is a linearly independent set in a vector space V. Show that if T : V -＞ W is a" one -to-one linear transformation, then {T(x+2y), T(2x-y)} is also linearly independent. (10 points)
#213191
(a) Find the characteristic polynomial of A. (5points)
#213192
(b) Find an invertible matrix P such that p-1 AP is diagonal. (10 points)
#213193
8. Given line L: x=z-y=y-z in R3, let P(x,y,z) be the orthogonal projection of (x,y,z) on L. Find P(x,y,z). (10 points)
#213194
9. Let T : V → W be a linear transformation, where V and W are finite dimensional vector spaces. Show that T is onto if and only if there exists a linear transformation S : W-» V such that TS(w)= w for all w in W. (10 points)
#213195
Aufsatz Thema: Was erwarten Sie von unserern neuen Prasidenten A-Bian?
#213196
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