## Our first dip into a new way of thinking

Now let’s take the same two equations as last time, but view them in a slightly different way. Call this the column view of the system. $x\underbrace{ \begin{bmatrix}2 \\ -1 \end{bmatrix}}_\mathrm{first \ vector} +\ y \underbrace{ \begin{bmatrix}-1 \\ 2 \end{bmatrix}}_\mathrm{second \ vector} = \underbrace{ \begin{bmatrix}0 \\ 3 \end{bmatrix}}_{resultant \ \mathrm{vector}}$

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## In Media Res, or a running start

Let’s look at a system of two equations in two unknowns. We have encountered this topic many times in earlier years, and we have a number of ways to ‘solve’ the system. $2x - y = 0 \qquad \cdots$ (1) $-x + 2y = 3 \qquad \cdots$ (2)

Before we go on, let’s solve this system of equations in two different ways that we already know about.

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## Why Linear Algebra?

At first glance, Linear Algebra may seem an unusual offering in the high school curriculum. In my view, this discipline can play a valuable role in a student’s math career. Free of large crowds, or an AP framework, we are able…