JUst need someone to showme how to do this then it will defintly clarify the rest of the problems for me.. one of the few examples is
1- Show there exists a linear transofrmation T: R2→R3 such that T(1,1) = (1,0,2) and T(2,3) = (1,-1,4). What is T(8,11)?
Suppose T is that thransformation
T(1,0) = 3 T(1,1) - T(2,3) = (2, 1, 2)
T(0,1) = T(2,3) - 2 T(1,1) = (-1,-1, 0)
So the matrix M = (2, -1 ; 1, -1 ; 2, 0) does this job and so defines a linear
transformation with the required properties, hence a linear transformation
T exists with the required properties and is defined by the matrix M.
Hence T(8,11) = [M (8,11)']' = (5, -3, 16)
RonL