Add Tridiagonal LU Decomposition example to README

Author: onezerosix

README.md

@@ -1,17 +1,38 @@
 # misc-matlab-scripts
+
 A collection of MATLAB scripts.
 
 ### Table of Contents
-1. [Tridiagonal LU Decomposition Matrix Solver](#Tridiagonal-LU-Decomposition-Matrix-Solver)
+
+1. [Tridiagonal LU Decomposition Matrix Solver](#Tridiagonal-LU-Decomposition-Matrix-Solver)  
+  a. [Example usage](#Example-usage)
 
 ### Tridiagonal LU Decomposition Matrix Solver
+
 This script solves `Ax = d` for `x` using LU decomposition for the square tridiagonal matrix `A`.
 
-A square tridiagonal matrix `A` has the following structure:\
+A square tridiagonal matrix `A` has the following structure:  
 <img src="https://raw.githubusercontent.com/onezerosix/misc-matlab-scripts/master/pictures/tridiag_lu_decomp_A.png" width="40%" alt="matrix A">
 
-The `a`, `b` and `c` variables are used as vector inputs for the script. The values must meet the following criteria for the script to work:\
+The `a`, `b` and `c` variables are used as vector inputs for the script. The values must meet the following criteria for the script to work:  
 <img src="https://raw.githubusercontent.com/onezerosix/misc-matlab-scripts/master/pictures/tridiag_lu_decomp_A_conditions.png" width="50%" alt="matrix A conditions">
 
-The output includes vector `x` and vector `z` such that `z = Ux`. It also includes vectors `alpha` and `beta` such that:\
+The output includes vector `x` and vector `z` such that `z = Ux`. It also includes vectors `alpha` and `beta` such that:  
 <img src="https://raw.githubusercontent.com/onezerosix/misc-matlab-scripts/master/pictures/tridiag_lu_decomp_LU.png" width="70%" alt="L and U matrices">
+
+##### Example
+```
+>> [alpha, beta, z, x] = tridiag_lu_decomp([2;2;2;2;2], [1;1;1;1;1], [1;1;1;1;1], [3;4;4;4;3])
+
+alpha =
+    2.0000    1.5000    1.3333    1.2500    1.2000
+
+beta =
+         0    0.5000    0.6667    0.7500    0.8000
+         
+z =
+    3.0000    2.5000    2.3333    2.2500    1.2000
+
+x =
+     1     1     1     1     1
+```