(Solved):     plz explain In \( \mathbb{P}_{2} \), find the change-of-coordinates matrix from ...

 

 

plz explain

In \( \mathbb{P}_{2} \), find the change-of-coordinates matrix from the basis \( B=\left\{1-2 t+t^{2}, 3-5 t+4 t^{2}, 2-2 t+5 t^{2}\right\} \) to the standard basis \( C=\left\{1, t, t^{2}\right\} \). Then find the \( B- \) coordinate vector for \( -1+2 t \) In \( P_{2} \), find the change-of-coordinates matrix from the basis \( B=\left\{1-2 t+t^{2}, 3-5 t+4 t^{2}, 2-2 t+5 t^{2}\right\} \) to the standard basis \( C=\left\{1, t t^{2}\right\} \). \[ \begin{array}{c} \mathrm{P} \\ \mathrm{C}-\mathrm{B} \end{array} \] (Simplify your answer.) Find the B-coordinate vector for \( -1+2 \mathrm{t} \) \( [x]_{B}= \) (Simplify your answer) Let \( A=\left\{a_{1}, a_{2}, a_{3}\right\} \) and \( B=\left\{b_{1}, b_{2}, b_{3}\right\} \) be bases for a vector space \( V \), and suppose \( a_{1}=2 b_{1}-b_{2}, a_{2}=-b_{1}+b_{2}+b_{3}, a_{3}=b_{2}-5 b_{3} \). a. Find the change-of-coordinates matrix from \( A \) to \( B \). b. Find \( [x]_{B} \) for \( x=5 a_{1}+6 a_{2}+a_{3} \) a. \( P= \) \( B \leftarrow A \)