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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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8. Given line L: x=z-y=y-z in R
3
, let P(x,y,z) be the orthogonal projection of (x,y,z) on L. Find P(x,y,z). (10 points)
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5. Let T : P2 → R2 be deflned by T(a+bx+cx2) = (a-b,c+a) and B={1, x,x2}，D={(1,-1)，(0，1)}. Find the matrix of T corresponding to the ordered bases B and D. (10 points)
#213190
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)
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(a) Find the characteristic polynomial of A. (5points)
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(b) Find an invertible matrix P such that p-1 AP is diagonal. (10 points)
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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)
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