Let e1 = (1,0), e2 = (0,1), x1 = (-8,7) and x2 = (-1,5)

Question

Let T = R^2 --> R^2 be a linear transformation that sends e1 to x1 and e2 to x2If T maps (8,7) to the vector y..

y = ?

1. Enter your answer as an ordered pair, such as (1,2)

Answer 1

(8,7) = 8(1,0) + 7(0,1)

So, T(8,7) = T(8(1,0)) + 7(0,1)) = T(8(1,0)) + T(7(0,1)) = 8T(1,0) + 7T(0,1) = 8(-8,7) + 7(-1,5) = (-71, 91) = y