Let V be the vector space P(t) of all polynomials in t over R, with inner product defined by (f(t), g(t)) = S, f(t)g(t) dt. Let W be the subspace P2(t) of V. (a) Show that B (b) Find the projection of...

Let V be the vector space P(t) of all polynomials in t over R, with inner product defined by<br>(f(t), g(t)) = S, f(t)g(t) dt. Let W be the subspace P2(t) of V.<br>(a) Show that B<br>(b) Find the projection of f(t) = t³ onto W.<br>{1, 2t – 1,6t? –- 6t + 1} is an orthogonal basis for W.<br>|<br>

Extracted text: Let V be the vector space P(t) of all polynomials in t over R, with inner product defined by (f(t), g(t)) = S, f(t)g(t) dt. Let W be the subspace P2(t) of V. (a) Show that B (b) Find the projection of f(t) = t³ onto W. {1, 2t – 1,6t? –- 6t + 1} is an orthogonal basis for W. |

Jun 04, 2022

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Let V be the vector space P(t) of all polynomials in t over R, with inner product defined by (f(t), g(t)) = S, f(t)g(t) dt. Let W be the subspace P2(t) of V. (a) Show that B (b) Find the projection of...

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