Linear mapping/Basis/(0,1,2) to (3,-2) and (1,4,1) to (1,0) and (2,1,3) to (7,2)/(3,-5,4)/Exercise

Let a linear mapping

$\phi :{ℝ}^3⟶{ℝ}^2$

satisfying

$\phi \left(\begin{array}{c}0\\ 1\\ 2\end{array}\right)=\left(\begin{array}{c}3\\ -2\end{array}\right),\phi \left(\begin{array}{c}1\\ 4\\ 1\end{array}\right)=\left(\begin{array}{c}1\\ 0\end{array}\right),\text{ and }\phi \left(\begin{array}{c}2\\ 1\\ 3\end{array}\right)=\left(\begin{array}{c}7\\ 2\end{array}\right)$

be given. Compute

$\phi \left(\begin{array}{c}3\\ -5\\ 4\end{array}\right).$

Create a solution