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
Dwindl
e
What three words in the English language start with “dw….”?
Determinants
2 by 2 determinant
D
3 2
Evaluate : 
6 1
Evaluate :
4 2
5 3
a b
c
d
 ad  bc
Cramer’s Rule
ax  by  s
The solution to the system 
is given by
cx  dy  t
Dy
Dx
x
y
D
D

a b
s b
where D 
, Dx 
,
c d
t d

Dy 
a s
c
t
Cramer’s Rule
Solve the following system of equations using Cramer’s Rule.
2x  4 y  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
f a
i
e
f
h
i
b
d
f
g
i
c
d
e
g h
OR
a b
D d
e
g h
c
f  d
i
b c
h
i
e
etc…
a c
g
i
f
a b
g h
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”?