Final answer:
To find T(3,4), set up a system of equations using the given information and solve for the constants (a,b) and (c,d) of the linear transformation. Substitute (3,4) into the linear transformation to get T(3,4).
Step-by-step explanation:
To find T(3,4), we need to first determine the linear transformation for T. We can use the given information to set up a system of equations.
Let's assume the linear transformation T is of the form T(x,y) = (a,b)x + (c,d)y, where (a,b) and (c,d) are constants. Using the given information, we get the following equations:
T(2,3) = (4,5): (a,b)2 + (c,d)3 = (4,5)
T(1,2) = (3,4): (a,b)1 + (c,d)2 = (3,4)
Solving this system of equations will give us the values of (a,b) and (c,d). Once we have these values, we can substitute (3,4) into the linear transformation and calculate T(3,4).