Let e1 1 0 e2 01 x1 14 and x2 1 8 Let TR2 rightarrow R2
Let e_1 = (1, 0), e_2 = (0,1), x_1 = (-1,4), and x_2 = (-1, -8). Let T:R^2 rightarrow R^2 be a linear transformation that sends e_1 to x_1 and to X_2 If T maps (7, 7) to the vector y, then y = ().
Solution
T(1,0) = (-1,4)
T(0,1) = (-1,-8)
T(7,7) = T(7(1,0) + 7 (0,1)) = 7* T(1,0) + 7* T(0,1) = 7*(-1,4) + 7 (-1,-8) = (-14,-28)
