README.md

# linear_algebra

| size of A | norm(error) |
|-----------|-------------|
|  3 | 12.0406
|  4 | NaN |
|  5 | inf |
|  6 | 162.541 |
|  7 | 36.517 |
|  8 | NaN |
|  9 | 30.745 |
| 10 | 716.512 |

Problem 2

k1 = 10; k2 = 20; k3 = 20; k4 = 10;

%N/m

m1 = 1; m2 = 2; m3 = 4; 

%kg

a = [(k1+k2)/m1 -k2/m1 0; -k2/m2 (k2+k3)/m2 -k3/m2; 0 -k3/m3 (k3+k4)/m3]

eigen = eig(a)

eigenvalues = 
    40.5220
   14.4090
    2.5690
    
Natural Frequency =
   6.3657
    3.7959
    1.6028


Part 2

[(2-0.36i) -1 0 0; 

-1 (2-0.36i) -1 0; 

0 -1 (2-0.36i) -1; 

0 0 -1 (2-0.36i)]      *    [y1;y2;y3;y4] =0

| # of segments | largest | smallest | # of eigenvalues |
| --- | --- | --- | --- |
| 5 | 3.17 | 1.03| 4 |
| 6 | 6.51|1.52 |5|
| 10 | 12.8|3.36|9 |