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bonfire09
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Homework Statement
Problem is assuming the mapping T: P2---->P2 defined by T(a0+a1t+a2t2)=3a0+(5a0-2a1)t+(4a1+a2)t^2 is linear. Find the matrix representation of T relative to Basis B={1,t,t^2}.
The part that I am confused on is when I go plug in the basis values T(1),T(t),and T(t^2)? I don't know how to do it?
Homework Equations
The Attempt at a Solution
So to find T(1) its just T(1+0t+0t2)=3a0+5a0tTo find T(t) is just T(0+a1(t)+0T2)=3(0)+(5(0)-2a1)t+(4a1+0)t^2=-2a1t+4a1t^2
T(t^2)= T(0+0t+a2t^2)=3(0)+(5(0)-2(0))t+(4(0)+a2)t^2=a2T2
Usually in lots of books they omit steps like these and I'm trying to figure them out. Is this a correct way?