Question

线性变换T(a,b,c)=(2a-b,b+c,a),求在基e1=(1,0,0),e2=(0,1,0),e3=(0,0,1

Answer 1

T(e1,e2,e3)

=(Te1,Te2,Te3)

= ((1,0,1),(-1,1,0),(0,1,0))

= (e1+e3,-e1+e2,e2)

= (e1,e2,e3)K

K =

1 -1 0

0 1 1

1 0 0