第二章1已知线性变换
矩阵及其运算
x12y12y2y3x23y1y25y3x33y12y23y3
求从变量x1x2x3到变量y1y2y3的线性变换解由已知
x1221y1x315yx2323y223
故
1y1221x1749y1y315x637yy2323x2324y2332
y17x14x29x3y26x13x27x3y33x12x24x3
2已知两个线性变换
x12y1y3x22y13y22y3x34y1y25y3
解由已知
y13z1z2y22z1z3y3z23z3
求从z1z2z3到x1x2x3的线性变换
x1201y120131x232y23220x2415y241501230z11z23z3
f613z11249z210116z3
x16z1z23z3所以有x212z14z29z3x310z1z216z3
111123111B124求3AB2A及ATB3设A111051
解
1111231113AB2A311112421111110511110581112132230562111217202901114292111123058AB111124056111051290
T
4计算下列乘积4317112325701
解
43174×73×21×13512321×72×23×1657015×77×20×149
3212321
f解
312321×32×23×1101
231123
解
2×12×2221121×11×2133×13×23
31301212
426
1421400113414
解
1214001r