math final

L fomrula

(made thorugh L multipliers)

U fomrula

use multiples of non-subject R multipliers

A trnaspose

guass jordan method to find inverse A

steps to chekc linear dependency

nul A =

col(A)=

solving hihger order system steps

1, rearragne for highest order
2. set x1, x2 etc equal to x’, x’’, etc
3. beginning at x’, set x’ = x’1
4. plug back in
5. make veraval vector of x1', x2' etc values over fromula, plug in vlaues ot make matrix

step 1

step2

step 3

last step

final formula?

for imaginary eigens

hwo to fidn the last part for a repeated eigen vlaue

(a-b)³

quadratic fomrula

repeated eigenvlaues fprmula

2×2 reduction

|a+bi|² 

a²+b²