Linear Transformations and Matrices

[hkus10]

Let L:P1 >> P1 be a linear transformation for which we know that L(t + 1) = 2t + 3 and L(t - 1) = 3t -2
a) Find L(6t-4)
I just want to check the way to calculate this question.
Is L(6t - 4) equal to 6*3t - 4*2 = 18t - 8? if not, how to calculate it?

 

[Dick]

Not. Why would you think that would be a 'way to calculate it'? Is there any logic behind that at all? You want to express 6t-4 as a combination of things you know how to calculate, like t+1 and t-1. Write 6t-4=A*(t+1)+B*(t-1). Find A and B.