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Dgray101

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## Homework Statement

(ii) S ◦ T will be a linear transformation from P4 to R2. Write a formula for the value S(T (a4t4 + a3t3 + a2t2 + a1t + a0)) using the given formulas for T,S and use this to compute the matrix [S ◦T]B′′,B. (10p)

B'' = {e1 e2}

B' = {t4, t3, t2, t,1}

T: P4--> M2x2

T(a4t4 + a3t3 + a2t2 + a1t + a0) = ( (a0 +a4 +2a2) (-a1 + a3 - a2) )

( (a1+a3+a2) (a0-a4) )

S:M2x2 ---> R2

S( x1A1 + x2A2 +x3A3 + x4A4 ) = (x1 +x2)

(x3-x4)

Where A1=[1 0 ,0 -1] A2= [ 1 0, 0 1] A3= [0 1, -1 0] A4 = [0 1, 1 0]

## Homework Equations

## The Attempt at a Solution

I don't quite understand how we can get the linear transformation S(T) so be in the desired form. Because we get S ( 2x2 matrix) but the definition of S is not this?
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