- Earlier, a reading question asked you to solve the system of equations
\begin{align*}
2x_1 + 3x_2 - x_3&= 0\\
x_1 + 2x_2 + x_3&= 3\\
x_1 + 3x_2 + 3x_3&= 7
\end{align*}
Use a linear combination to rewrite this system of equations as a vector equality.
- Find a linear combination of the vectors
\begin{equation*}
S=\set{\colvector{1\\3\\-1},\,\colvector{2\\0\\4},\,\colvector{-1\\3\\-5}}
\end{equation*}
that equals the vector $\colvector{1\\-9\\11}$.
- The matrix below is the augmented matrix of a system of equations, row-reduced to reduced row-echelon form. Write the vector form of the solutions to the system.
\begin{equation*}
\begin{bmatrix}
\leading{1}&3&0&6&0&9\\
0&0&\leading{1}&-2&0&-8\\
0&0&0&0&\leading{1}&3
\end{bmatrix}
\end{equation*}