Some Useful Mathematical Formulas - Digital Signal Processing: Fundamentals and Applications - page 830

3 3 determinant:

a 11 a 12 a 13

D ¼ a 21 a 22 a 23

a 31 a 32 a 33

(G.46)

a 11

þð 1 Þ

a 12

þð 1 Þ

a 13

a 22 a 23 a 21 a 23 a 21 a 22

1 þ 1 1 þ 2 1 þ 3

¼ð 1 Þ

a 32 a 33 a 31 a 33 a 31 a 32

¼ a 11 ða 22 a 33 a 23 a 32 Þa 12 ða 21 a 33 a 23 a 31 Þþa 13 ða 21 a 32 a 22 a 31 Þ

Solution for two simultaneous linear equations:

ax þ by ¼ e
cx þ dy ¼ f

(G.47)

The solution is given by

eb
f d

x ¼ D 1 ¼ ed bf

ad bc D ¼

(G.48)

ab
cd

ae
cf

y ¼ D 2 ¼ af ec

ad bc D ¼

(G.49)

ab
cd