SOLVING LINEAR SYSTEMS

SOLVING LINEAR SYSTEMS


71 272 73 0 t x o

72 4 3 4 72 16
73 3 73 3




I 73 3




AUGMENTED MATRIX OF LINEAR SYSTEMS
a 2 1 1 O
o 1 y 4 Back Substitution
O 0 11 3

N F
O H t
I m non zero
pivot
I t
O O H any value sot unique

ex 272 73 0 H e 2 1 É
47 4
272
52
8 3
93
8
9
12
13
818
4 5 91 9
2

, ROW REDUCTION ALGORITHM
12 72 473 4 129
4
4 11 13 372 13 3 9 3


3 124 13 73 3 13

t 73 0

x 472 4 124 72 16
g 73 3




72 16




ELEMENTARY ROW OPERATIONS

Me Add a multiple of any vow to any other
VOW
1221 Exchange 2 vows
123 Scale any row by non zero number


exe 372 74 7
1
427 3 0 t É
72 373 2 4 0 1 1 3 2 10