Answer
0
Work Step by Step
For f and g in C[0,1], the inner product is defined as follows
$\langle f,g\rangle=\int_0^1f(t)g(t)dt=\int_0^1(5t-3)(t^3-t^2)dt=\int_0^1(5t^4-8t^3+3t^2)dt=\left[t^5-2t^4+t^3\right]_0^1=0$
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