README.md

# Linear_algebra

2) LU-decomposition function is presented in the lu_tridiag.m file. 

3) The function was tested using test_arrays.m file. 

4) Test your function on the matrices A3, A4, ..., A10 generated with test_arrays.m Solving for b=ones(N,1); where N is the size of A. In your README.md file, compare the norm of the error between your result and the result of AN\b.

To calculate the error in matlab, I used the norm function by typing in NORM' at the end of my code.

| size of A |     norm(error)      |
|-----------|----------------------|
|     3     |    2.3414572118      |
|     4     |    1.508931741       |
|     5     |    2.7183537012      |
|     6     |    2.995245881       |
|     7     |    2.1975878506      |
|     8     |    2.2726826         |
|     9     |    1.256568519597    |
|     10    | 0.0000000000000001092|

5) These are the lambda and omega values found through the slender_column.m file:

| lambda    |     Omega      |
|-----------|----------------|
|  2.5690   |     1.6028     |
|  14.4090  |     3.7959     |
|  40.5220  |     6.3657     |

These are the eigenvalues that were produced through the Pole_Vaulting.m file:

| # of segments | largest | smallest | # of eigenvalues |
| ------------- | ------- | -------- | ---------------- |                                 |
|       5       | 3.6163  | 0.3803   |        4         |
|       6       | 3.7310  | 0.2669   |        5         |
|      10       | 3.9018  | 0.0976   |        9         |