Are these set of functions linearly independent? If they are dependent, state the relation.

1. f1(x) = 2x − 3, f2(x) = x^2 + 1, f3(x) = 2x^2 − x

2.f1(x) = 2x − 3, f2(x) = 2x^2 + 1, f3(x) = 3x^2 + x

Question

Are these set of functions linearly independent? If they are dependent, state the relation.

1. f1(x) = 2x − 3, f2(x) = x^2 + 1, f3(x) = 2x^2 − x

2.f1(x) = 2x − 3, f2(x) = 2x^2 + 1, f3(x) = 3x^2 + x

turingtest · Answer

make a matrix of the coefficient vectors|dw:1329543360004:dw|you have many methods to check for a linearly dependent set of vectors, but taking the determinant is probably easiest here