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epkid08

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## Homework Statement

Let [itex]g_1(t) = t - 1[/itex] and [itex]g_2(t)= t^2+t[/itex]. Using the inner product on [itex]P_2[/itex] defined in example 10(b) with [itex]t_1=-1,t_2=0,t_3=1[/itex], find a basis for the orthogonal complement of [itex]Span(g_1, g_2)[/itex].

## Homework Equations

From example 10(b)

[itex]\langle p, q \rangle = \sum_{i=1}^{k+1} p(t_i)q(t_i)[/itex]

[itex](p,q)\in P_2[/itex]

## The Attempt at a Solution

Well the orthogonal complement of [itex]span(g_1,g_2)[/itex] will be [itex]x[/itex] such that [itex]x\cdot (c_1g_1 + c_2g_2) = 0[/itex], but how can I find the basis for that set? And why and where do we need to use inner product? I am confused

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