WeBWorK Standalone Renderer

(a) Let

$v_1 = \left[\begin{array}{c} -9\cr 2 \end{array}\right] \quad v_2 = \left[\begin{array}{c} -10\cr 9 \end{array}\right] \quad S = \left[\begin{array}{cc} -11 &-5\cr -13 &-6 \end{array}\right] \quad$

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

$\lbrace 1, 1+x, 1+x +x^2, 1+x+x^2+x^3 \rbrace$ .

$A =$

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

You can earn partial credit on this problem.