第二章
1.已知线性变换:
矩阵及其运算
x1=2y1+2y2+y3 x2=3y1+y2+5y3, x3=3y1+2y2+3y3
求从变量x1,x2,x3到变量y1,y2,y3的线性变换.
解由已知:
x1 221 y1
x = 315 y , x2 323 y2
2 3
故
1
y 1 221 x1 7 49 y1 y = 315 x = 63 7 y , y2 323 x2 32 4 y2
3 3 2
y1= 7x1 4x2+9x3
y2=6x1+3x2 7x3. y3=3x1+2x2 4x3
2.已知两个线性变换
x1=2y1+y3
x2= 2y1+3y2+2y3, x3=4y1+y2+5y3
解由已知
x1 201 y1 201 31 x = 232 y = 232 20 x2 415 y2 415 0 1
2 3
0 z1
1 z2 3 z3
y1= 3z1+z2
y2=2z1+z3, y3= z2+3z3
求从z1,z2,z3到x1,x2,x3的线性变换.