# Transcribed Image Text: Consider the following where c,, C2, Cz and ca are constants. c,(1 – 4x) + c2(9x + x2

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one of the polynomials as a linear combination of the others. (If the set is linearly independent, enter INDEPENDENT. If the set is linearly dependent, enter your answer as an equation using the variables f, g, h, and j as they relate to the question.) |

Transcribed Image Text: Consider the following where c,, C2, Cz and ca are constants.

c,(1 – 4x) + c2(9x + x2 – x) + c3(1 + x2 + 4x³) + c4(9 + 4x + 9x³) = 0

Find c,, C2, ca, and c. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. If only the trivial solution exists, enter the

trivial solution (c,, c2, C3, C4) = (0, 0, 0, 0).

(C1, C2, C3, C4) =

Consider the following.

{f{x) = 1 – 4x, g(x) = 9x + x2 – x³, 1 + x² + 4x³, h(x) = 9 + 4x + 9x³} in P,

Test the set of polynomials for linear independence. If it is linearly dependent, express one of the polynomials as a linear combination of the others. (If the set is

linearly independent, enter INDEPENDENT. If the set is linearly dependent, enter your answer as an equation using the variables f, g, h, and j as they relate to the

question.)

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