I'm taking a linear algebra class now, and I was introduced to vector equations. Consider the system
$
\left\{ \begin{array}{rcl}
x-4y &=& 8\\
2x+3y &=& 6\\
\end{array}
\right.$
I want to understand why I can factor out the x and y variables to create the vector equation $x\begin{bmatrix} 1 \\ 2 \end{bmatrix}+y\begin{bmatrix} -4 \\ 3 \end{bmatrix}=\begin{bmatrix} 8 \\ 6 \end{bmatrix}$
are $x$ and $y$ scalars here? Is the column vector $\begin{bmatrix} 1 \\ 2 \end{bmatrix}$ the same as the vector $\left< 1, 2\right>$? And lastly, how does this notation help me solve for solutions?
