Question

Consider the following functions. f1(x) = x, f2(x) = x-1, f3(x) = x+4 g(x) = c1f1(x)...

Consider the following functions.
f1(x) = x, f2(x) = x-1, f3(x) = x+4
g(x) = c1f1(x) + c2f2(x) + c3f3(x)
Solve for c1, c2, and c3 so that g(x) = 0 on the interval (−∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.)
{c1, c2, c3} =?


  

Determine whether f1, f2, f3 are linearly independent on the interval (−∞, ∞).
linearly dependent or linearly independent?  

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