README.md

# linear_algebra
#Homework 5
2.) 

The LU decomposition is excuted by the functions `lu_tridiag.m`.
The function `solve_tridiag.m` solves the x vector in the equation Ax = B
The `test_array.m` function then creates the matrixs that will be decomposed.

3.)

The table below compares the error between the created code and AN\b

| size of A | norm(error) |
|-----------|---------------------------------|
| 3         |  2.341457211866148746537419356  |
| 4         |  1.5089317413322578254053496494 |
| 5         |  2.718353701243559239486557999  |
| 6         |  2.9952458816401601460199799476 |
| 7         |  2.1975878506014523416922656907 |
| 8         |  2.2726826857500208589613066579 |
| 9         |  1.2565685195978946175898727233 |
| 10        |  0.0000000000000001092738104726 |

#Spring Mass System
[This file shows the caclations to arrive at a final matrix.]

(Spring Mass System.PNG)