Let T:R3→R3 be a linear transformation such that T(1,0,0)=(2,4,-1),T(0,1,0)=(1,3,-2),and T(0,0,1)=(0,-2,2) Find :-

Question

1-T(0,3,-1)

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Answer 1

Remember what happens if you multiply a Cartesian unit unit vector by a matrix.

For example,

Multiply...

3 4 * 1 = 3*1 + 4*0 = 3

1 7 0 1*1 + 7*0 1

And

3 4 * 0 = 3*0 + 4*1 = 4

1 7 1 1*0 + 7*1 7

So the matrix from your problem, is going to be

2 1 0

4 3 -2

-1 -2 2

From here simply multiply the vector (0, 3, -1) by the matrix above. You'll have your answer.

Hope this helps.