updated week 9 announcement: point to linear algebra

_announcements/week-9.md

@@ -4,12 +4,14 @@ week: 9
 date: 2024-03-18
 ---
 
-A common problem is to find the roots of an equation. We will develop
-two algorithms to find roots numerically. The *bisection* algorithm is
-a simple and robust approach that exemplifies how to go from imagining
-a solution ("how would I solve this problem?") to an actual
-implementation. We then will develop a much faster but less robust
-algorithm known as *Newton-Raphson*. In both cases we will initially
-restrict ourselves to 1D problems but we will later extend
-Newton-Raphson to arbitrary dimensions (once we learned how to solve
-matrix problems).
+A common problem is to **find the roots** $$x_0$$ of an equation,
+$$f(x_0)=0$$. We will develop two algorithms to find roots
+numerically. The *bisection* algorithm is a simple and robust approach
+that exemplifies how to go from imagining a solution ("how would I
+solve this problem?") to an actual implementation. We then will
+develop a much faster but less robust algorithm known as
+*Newton-Raphson*. In both cases we will initially restrict ourselves
+to 1D problems. We then find that we can easily extend Newton-Raphson
+to arbitrary dimensions to solve $$\mathbf{f}(\mathbf{x}_0) =
+\mathbf{0}$$ but we will need to learn how solve *matrix equations*,
+which directly leads us into **linear algebra**.