A (a matrix) = 1 3 0 2 1 -1
A: R^3 ----> R^2 linear
v -----> Av
Let B = {(1,0,2),(0,1,-1),(2,1,3)} basis of R^3, C= {(2,1),(3,2)} basis of R^2
Compute the matrix A ith respect to B of R^3 and C of R^2
I have the solution but I don't really uunderstand the workings.
Sol: A(1,0,2) = (1,0) = a11 (2,1) + a21(3,2) = 2(2,1) - (3,2)
A(0,1,-1) = (3,2) = 0(2,1) + 1(3,2)
A(2,1,3) = (5,2) = 4(2,1) - 1(3,2)
this gives the matrix:
2 0 4
-1 1 -1
The main bit I don't understand is why (1,0) and (3,2) and (5,2) are chosen??