10.3 Determinants and Cramer’s Rule
What three words in the English language start with “dw….”?
10.3a Determinants and Cramer’s Rule
Dwarf
Dwell
Dwind
le
What three words in the English language start with “dw….”?
Determinants
2 by 2 determinant
a b
D
 ad  bc
c d
3 2
Evaluate : 
6 1
4 2
Evaluate :
5 3
Cramer’s Rule
ax  by  s
The solution to the system 
is given by
cx  dy  t
Dx
x
D
y
Dy
D

a b
s b
a s
where D 
, Dx 
, Dy 
c d
t d
c t

Cramer’s Rule
Solve the following system of equations using Cramer’s Rule.
2x  4y 16

3x  5y  9
Cramer’s Rule
Solve the following system of equations using Cramer’s Rule.
3x  2y  0

5x 10y  4
Determinants
3 by 3 determinant
a b
D d e
g h
c
e
f a
h
i
f
d
b
i
g
f
d e
c
i
g h
OR
a b
D d e
g h
c
b c
a c
a b
f  d
e
f
h i
g i
g h
i
etc…
Determinants
1 3 -2
Evaluate : 6 1 -5
8 2 3
Determinants
3 -9 4
Evaluate : 1 4 0
8 -3 1
Cramer’s Rule
Cramer’s Rule
Let’s apply Cramer’s Rule to solve a system of three equations.
 2x  y  z  8

2x  3y  z  4

4 x  2y  3z  3
Cramer’s Rule
Let’s apply Cramer’s Rule to solve a system of three equations.
x  2y  5

4 x  8y  6
Cramer’s Rule
Let’s apply Cramer’s Rule to solve a system of three equations.
 2x  y  z  8

2x  3y  z  4

4 x  2y  3z  3
10.3a Determinants and Cramer’s Rule
What two words in the English language end with “…-gry”?
10.3 Determinants and Cramer’s Rule
Angry
Hungry
p.767 #25, 27, 33-37 odd
What two words in the English language end with “…-gry”?