determine the coordinate vector of the polynomial p 13x8x2 i

determine the coordinate vector of the polynomial p= -1+3x-8x^2 in terms of the base {x+3x^2, 3-2x-x^2, 4+4x+2x^2}

Solution

the coordinate vectors entries a,b,c meet the following criterion:

a(x+3x^2) +b(3-2x -x^2) +c(4 +4x +2x^2) = -1+3x-8x^2

x^2(3a -b+2c) +x(a -2b+4c) +( 3b +4c) = -1+3x-8x^2

we have equations:

3a -b +2c =-8

a-2b+4c = 3

3b +4c = -1

Solve the system of equations:

Coordinate vector : (a, b, c) = ( -19/5 , -39/25 , 23/25)