Question

Find the matrix representation of T using the base
1 0
, ;
0 1
 

Answer 1

Answer:

I'm not sure what to start with on this problem. I think that I should be plugging in BB. But, then I'm not sure where BB belongs within the equation. Do I need to plug in the entire vector BB at once? For example, let 1=a01=a0, x=a1x=a1, and x2=a2x2=a2? That would leave me with the answer 1+x−2x2−3x31+x−2x2−3x3.

Step-by-step explanation:

Let T: P2→P1T: P2→P1 be a linear transformation defined by

T(a0+a1x+a2x2)=(a0+a1)−(2a1+3a2)x.T(a0+a1x+a2x2)=(a0+a1)−(2a1+3a2)x.

Find the matrix TT with respect to the standard bases B={1,x,x2}B={1,x,x2} and B′={1,x}B′={1,x} for P2P2and P1P1.