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Cramer’s rule
Determinants
• Determinants are square arrays of
numbers.
• Each number in the array is an element
• A two by two array is called a second
order determinant. (2 rows and 2 columns)
Second Order Determinants
• This is the formula for
solving a second order
determinant.
• To find the value of a
second order determinant
you take the difference in
the cross products. Going
from top left times bottom
right subtracted by the
bottom left times the top
left as shown here------->.
Example 1
• Find the value of
the determinant.
3(5) – 4(2)=
3
4
2
5
=7
Cramer’s Rule
• Another method for solving
systems of equations
• Cramer’s Rule utilizes
determinants
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Example 2
• Use Cramer’s Rule to solve
the system of equations.
6x + 7y = -9
x - y =5
A = 6, B = 7, E = -9
C =1, D = -1, F = 5
Answer: ( 2, -3)
X=
-9
7
5
-9
5
-1
y= 1
5
6
7
6
7
1
-1
1
-1
Example 3
Two sides of a
parallelogram are
contained in the lines
whose equations are
3x – 2y = -24 and
5x + y = -14. Find the
coordinates of a
vertex of the
parallelogram.
A =3, B = -2, E = -24,
C = 5, D = 1, F = -14
Answer: ( -4, 6)
-24
-2
3 -24
x= -14
1
y= 5 -14
3
-2
3
-2
5
1
5
1
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