Question

已知F^3的线性变换x(a,b,c)=(a+b,a-c,c)求在基x1(1,0,0)x2(1,1,0)x3(1,1,1)下的矩阵

(a,b,c)属于 f^3

Answer 1

x=(1 1 0 )
1 0 0
0 -1 1

(1 1 0 ) (1 1 1) =(1 2 2)
1 0 0 0 1 1 1 1 1
0 -1 1 0 0 1 0 -1 0

追问

能说的详细点吗。看不懂

追答

= = 我错了。。。想了下应该这么做的

X(x1,x2,x3)=(x1,x2,x3)K
X(x1,x2,x3)=(2 0 1 )
1 -1 1
0 -1 1
(x1,x2,x3)= (1 1 1)
0 1 1
0 0 1
k=(2 0 1 ) (1 -1 0) =(2 -2 1)
1 -1 1 0 1 -1 1 -2 2
0 -1 1 0 0 1 0 -1 2