Suppose T : C^2 → C^3 is a linear map so that T(1, 1) = (1, 0, 2) and T(2, 3) = (1,−1, 4). What is T(8, 11)?

Which of the following functions are linear? Justify your answer in a comprehensible manner. In the case of a linear function, determine the basis of the image and the core and also the associated dimensions in a comprehensible manner. (i) fi: R R, (a, b,c)"() (ii) fa : R - R. (:) ) (ii) f; : R → R', (:) ) (iv) fa : R → R', (a, b,c) (1,1, 1)"

Only b question

Consider a function z = F(u(s, t), v(s, t)) where F, u, and u are differentiable and u(8, 6) = -1, v(8, 6) = 2, u, (8, 6) = 5, u, (8, 6) = 9, vs(8, 6) = −3, v₁(8, 6) = 4, Fu(-1,2) = -4, and F(-1,2)= -10. Compute and when s = 8 and t = 6 dt