(y1,y2,y3)'=
[2 -2 -3]
[1 1 1]
[1 3 -1]
(z1,z2,z3)'=
[1 0 2]
[0 -1 1]
[2 3 4]
*(y1,y2,y3),
所以
(z1,z2,z3)'=
[1 0 2]
[0 -1 1]
[2 3 4]
*(y1,y2,y3)
=
[1 0 2]
[0 -1 1]
[2 3 4]
*
[2 -2 -3]
[1 1 1]
[1 3 -1]
*(x1,x2,x3)
=
[4,4,-5]
[0,2,-2]
[11,11,-7]
*(x1,x2,x3)
故x1,x2,x3到z1,z2,z3的线性变换是
z1=4x1+4x2-5x3
z2=2x2-2x3
z3=11x1+11x2-7x3