Mathematics

Linear Algebra: Introduction

[latexpage]

The quintessential linear algebra problem will ask for the solution of a set of linear equations.

  • Example: Find the solution $(x,y)$ for the linear system

$\begin{matrix}
3x-y=2 \\
2x+3=4
\end{matrix}$

  • There are two ways we can interpret the solution to these equations:
    • The point(s) at which these equations intersect when plotted as a line in $\mathbb{R}^2$
      • For our example, we can rewrite each equation in our system as a function $f(x)=y$ and plot each function on $\mathbb{R}^2$ to visualize the this interpretation of the solution:
    • If we rewrite the system as a vector equation, the solution becomes the set of scalar values that are multiplied with respective column vectors on the left hand side of the vector equation so that we obtain the right hand side

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Sources

  • Linear Algebra and its Applications, 3rd Edition. Gilbert Strang (1986)

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