一道线性代数题
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a)T(p) = [p(-1), p(0), p(1)] = [2, 5, 8]
b) 设T(p1) = y1 = [p1(-1), p1(0), p1(1)]
设T(p2) = y2 = [p2(-1), p2(0), p2(1)]
T(c1p1 +c2p2) = [c1p1(-1)+c2p2(-1), c1p1(0)+c2p2(0),c1p1(1)+c2p2(1)]
=c1 y1 + c2y2所以是线性变换
T(1) = (1, 1,1)
T(t) = (-1,0,1)
T(t^2)=(1,0,1)
b) 设T(p1) = y1 = [p1(-1), p1(0), p1(1)]
设T(p2) = y2 = [p2(-1), p2(0), p2(1)]
T(c1p1 +c2p2) = [c1p1(-1)+c2p2(-1), c1p1(0)+c2p2(0),c1p1(1)+c2p2(1)]
=c1 y1 + c2y2所以是线性变换
T(1) = (1, 1,1)
T(t) = (-1,0,1)
T(t^2)=(1,0,1)
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