Let T be a linear operator on R2 defined as follows on the standard basis of R2. T(1, 0) = (3, 2), T(0, 1) = (−1, 4). Find T(9, 4).

Answer 1

(9,4) = 9*(1,0) + 4*(0,1)
So,
T(9,4) = 9T(1,0)+4T(0,1)
= 9(3,2) + 4(-1,4)
= (27,18) + (-4,16)
= (23,34)