Linear algebra - transformation of matrix

[Eagerissac]

I was wondering if someone could explain why my answer 13 is incorrect?

I thought the matrix indicated that a = 1, b = 0. c = 2, and d = 1. So I substituted these values in the equation, giving me:

1 + (1 - 0 - 2 + 1) +(-2)^2 + (1 + 0 + 2 - 1)^3 and got 13. I'm not sure what I'm doing wrong and would appreciate help.

I'm not sure if I'm supposed to do anything with the x, x^2, x^3 variables?

 

[LCKurtz]

You want to leave the x's in the expression so you get a polynomial answer.

 

[Steven G]

You can think of the problem as the function T(a, b, c, d) = 1 + (a-b-c+d)x + (-c²)x² + (a+b+c-d)x³. The (-c)² can be replaced with c².

So T(a, b, c, d) = 1 + (a-b-c+d)x + (c²)x² + (a+b+c-d)x³

Then T(1, 0, 2, 1) = 1 + (1-0-2+1)x + (2²)x² + (1+0+2-1)x³
= 1 + (0)x + (4)x² + (2)x³ = 1 + 4x² + 4x³

Please let me know if this is clear.