Applications of Matrices and
Determinants (Cramer’s Rule)
(Section 7-7)
Essential Question: How do you find
the determinant of a square matrix?
Students will write a summary explaining when to
use each method and the steps for using each
method.
Essential Question: How do you find the determinant of a square matrix?
Students will write a summary explaining when to use each method and the steps for using each method.
Find the determinant of the matrix.
Example 1
Essential Question: How do you find the determinant of a square matrix?
Students will write a summary explaining when to use each method and the steps for using each method.
Find the determinant of the matrix.
Example 2
Essential Question: How do you find the determinant of a square matrix?
Students will write a summary explaining when to use each method and the steps for using each method.
Find the determinant of the matrix.
Example 3
Essential Question: How do you find the determinant of a square matrix?
Students will write a summary explaining when to use each method and the steps for using each method.
Cramer’s Rule is used when…
The coefficients are large or involve fractions or decimals.
If the denominator equals zero, then there is no solution.
0
no
Essential Question: How do you find the determinant of a square matrix?
Students will write a summary explaining when to use each method and the steps for using each method.
Use Cramer’s Rule to solve the linear system.
Example 4:
5x + 7y = 13
2x – 5y = 13
If solving for x then
replace x-column with
answer column
x=
Fill in
Denominator
First
A y
n c
s o
l
If solving for y then
replace y-column
with answer
column
13
13
x A
c n
o s
l
13
13
y=
5
7
5 7
2
-5
2 -5
x
c
o
l
y
c
o
l
x
c
o
l
y
c
o
l
Essential Question: How do you find the determinant of a square matrix?
Students will write a summary explaining when to use each method and the steps for using each method.
Use Cramer’s Rule to solve the linear system.
Example 5
9x + 4y = -6
3x – 5y = -21
Essential Question: How do you find the determinant of a square matrix?
Students will write a summary explaining when to use each method and the steps for using each method.
Use Cramer’s Rule to solve the linear system.
Example 6
5x + 7y = 13
2x – 5y = 13
Essential Question: How do you find the determinant of a square matrix?
Students will write a summary explaining when to use each method and the steps for using each method.
Solve using Cramer’s Rule.
Example 7
Essential Question: How do you find the determinant of a square matrix?
Students will write a summary explaining when to use each method and the steps for using each method.
Solve using Cramer’s Rule.
Example 8
Essential Question: How do you find the determinant of a square matrix?
Students will write a summary explaining when to use each method and the steps for using each method.
Homework: Page 556 (3-8 all) pg 567 (15-19 all)
pg 575 (171-173 all)
Essential Question: How do you find the determinant of a square matrix?
Students will write a summary explaining when to use each method and the steps for using each method.