(x1, x2) in R2:
(x1, x2) = c1v1 + c2v2
= c1 (1, 1) + c2 (1, 0)
= (c1, c1) + (c2,0)
= (c1+c2, c1)
we get
x1 = c1 + c2
x2 = c1
x1 = x2 + c2
c2 = x1 – x2
Again
(x1, x2) = c1v1 + c2v2
T is linear, so
T(x1, x2)= c1T(v1) + c2T(v2)
= c1(1, 2) + c2(3, 0)
= (c1, 2c1) + (3c2, 0)
= (c1 + 3c2, 2c1)
= (x2 + 3(x1 – x2), 2x2)
= (x2 +3x1 – 3x2, 2x2)
T(x1,x2)= (3x1 –2x2, 2x2) formula.
T(2,-4)= (3(2) –2(-4), 2(-4))
= (14,-8)