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If we are given that the first three Laguerre polynomials are the following: $$ mathcal{B}=left{1,1-mathrm{t}, 4-2 mathrm{t}+mathrm{t}^{2} ight) $$ Altogether, the polynomials form a basis

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If we are given that the first three Laguerre polynomials are the following: $$ \mathcal{B}=\left\{1,1-\mathrm{t}, 4-2 \mathrm{t}+\mathrm{t}^{2} ight) $$ Altogether, the polynomials form a basis of $P_{2}$. What are the coordinates of $p(t)=5+5 t-2 t^{2}$ with respect to B. Present the final answer through coordinate-vector notation, or by stating that "the coordinates of $P(t) $ with respect to the basis $B$ are CS.VS.13921

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