(a) Let

Find vectors

$u_1 =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$
$u_2 =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

in $\mathbb{R}^2$ such that $S$ is the transition matrix from $\lbrace v_1, v_2 \rbrace$ to $\lbrace u_1, u_2 \rbrace$.

(b) Let $P_4$ be the vectors space of all polynomials of degree less than four. Find the transition matrix $A$ representing the change of basis from the ordered basis

$\lbrace -12, -10x, 13x^{2}, -15x^{3} \rbrace$
to
$\lbrace 1, 1+x, 1+x +x^2, 1+x+x^2+x^3 \rbrace$.

$A =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

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