1. Using matrices with systems
You can use matrices to solve systems of
equations. This is most useful for large numbers
of equations, though we will only use 2 or 3
variables.
2. Example
1 1 3
2 1 1
x
y
AX = B
3
2 1
x y
x y
Matrix of
coefficients
Matrix of variables
Matrix of
sum or
difference
As all matrices:
4. Using with systems
1 1 1 1 1 1 3
2 1 2 1 2 1 1
x
y
1 1
AX B
A AX A B
A matrix times its own
inverse equals the identity
matrix, so it cancels.
The inverse must go
FIRST on both sides.
(Multiplication order
matters!)
5. Using with systems
(-4,-7)
1 1 3
2 1 1
x
y
4
7
x
y
6. Cramer’s Rule
Cramer’s Rule also allows you to solve systems
of equations using matrices. A matrix is set up
of just the coefficients, then one more matrix for
each variable.
8. Example, continued
Make a matrix for each variable by replacing a
column with the answers to each equation.
Use these numbers to
replace the x or y column.
6 3
11 2
xC
4 6
6 11
yC