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(Solved): 3)Let \( \beta=\left\{x+2, x-1, x^{2}+x+2\right\} \) be a basis for \( \mathbb{P}_{2} \), the vect ...



3)Let \( \beta=\left\{x+2, x-1, x^{2}+x+2\right\} \) be a basis for \( \mathbb{P}_{2} \), the vector space of polynomials of

3)Let \( \beta=\left\{x+2, x-1, x^{2}+x+2\right\} \) be a basis for \( \mathbb{P}_{2} \), the vector space of polynomials of degree 2 or less. a) Compute the following: \( [1]_{\beta},[x]_{\beta} \), and \( \left[x^{2}\right]_{\beta} \). b) Use the fact that the evaluation map is a linear tranformation and your work for part a) to find a formula for \( \left.\left[a+b x+c x^{2}\right]\right]_{\beta} \).


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