Consider the vector space \(P_5(t)\) whose elements \(p(t)\) are polynomials in \(t\) of degree less than or equal to 4. \[ p(t) =\alpha_0 +\alpha_1t + \alpha_2 t^2 + \alpha_3 t^3 +\alpha_4t^4\] Consider the subspace \(V_1\) of \(P_5(t)\) consisting of polynomials which are even functions of \(t\). What is the dimension of \(V_1\)? What is the vector space \(V_2\) such

that \( P_5(t) = V_1 \oplus V_2\). What is dimension of quotient space \(P(t)/V_1\)? Give a basis for \(P(t)/ V_1\).

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4727:Diamond Point

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