Question

find the coordinate vector [x]b of the vector x relative to the given basis b. b = {1 x x2, 1 3x 2x2, 4 x2} and x = -2 + 4x + 2x2

Answer 1

i think this answer

Explanation:

We want [a,b,c] with a, b, and c satisfying

[-1,2,4] = a[1,4,6] + b[0,1,-4] + c[0,0,1]

Equating components:

-1 = a

2 = 4a + b = -4 + b → b = 6

4 = 6a - 4b + c = -6 - 24 + c → c = 34

[-1,6,34] is the coordinate vector with respect to basis B