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*T(x,y,z)=(-x-y-z,x+y-5z,-3x-3y+3z) is a linear transformation.

S is the standard basis, S={e1,e2,e3} and B is another basis, B={v1,v2,v3} where:

e1=(1,0,0) e2=(0,1,0) e3=(0,0,1) v1=(1,1,1,) v2=(1,-1,0) v3=(0,1,-1)

- [T]S->S = [1 0 0

0 1 0

0 0 1]

-P B->S = [1 1 0

1 -1 1

1 0 -1]

-P S->B = [1/3 1/3 1/3

2/3 -1/3 -1/3

1/3 1/3 -2/3]

-[e2]B = P S->B.[e2]S

= (1/3,-1/3,1/3)

-[T(e2)]B =? what does this refer to? Do I have to refer to the equation in any part of these? as in the matrix [-1 -1 -1

1 1 -5

-3 -3 3]

Any help is greatly appreciated!