README.md

# linear_algebra
3.
size of A  | norm error
3          |
4          |


5. Solve spring mass system: 
M = (1  0  0 
     0  2  0 
     0  0  4)
K = (k1+k2  -k2     0   
     -k2    k2+k3  -k3  
      0      -k3   k3+k4)
K = ( 30  -20   0 
     -20   40  -20
       0  -20   30 )
Mx'' + Kx = 0

1*x1''+ 30*x1 - 20*x2 = 0
2*x2''- 20*x1 + 40*x2 - 20*x3 = 0
4*x3''- 20*x2 + 30*x3 = 0

k~ = ( 30    -14.2   0
      -14.2   20.16  -7.1
       0       -7.1   7.5 )
(k~ - (eigenvalue)I)*v = 0
det(k~ - (eigenvalue)I) = 0
eigenvalue = E

(30-E  -14.2      0 
-14.2  20.16-E  -7.1      = 0
   0    -7.1     7.5-E)


(30-E)(((20.16-E)*(7.5-E)) + 7.1(-7.1)) + 14.2(-14.2*(7.5-E)) 

(30-E)(100.79 + 12.66E + E^2) + -1512.3 - 201.64E
3023.7 + 379.8E + 30E^2 - 100.79E - 12.66E^2 -E^3 - 1512.3 - 201.64E
1511.4 + 77.37E + 17.34E^2 -E^3 = 0

E1 = 23.4
wn1 = 4.837m/s

6. 
# of segments | largest | smallest | # of eigenvalues 
5 
6
10