1. 4.7 Solving Systems using Matrix Equations and Inverses

2. Matrix Equation
A linear system can be written as a matrix equation AX=B
Constant matrix
Coefficient matrix
Variable matrix

3. Ex. 1 Write as a matrix equation.

4. Solving Matrix Equations
Suppose ax = b
How do you solve for x?
We cannot divide matrices, but we can multiply by the inverse.
A-1
AX = B
A-1
IX = A-1B
X = A-1B

5. Ex. 2 Solve using matrices.
AX = B
X = A-1B A
x = -7
y = -4 B
(-7, -4)

6. Ex. 3 Solve using matrices
y = 2
(5/7, 2)

7. Ex. 4 Solve using matrices
y = -1
z = -2
(2, -1, -2)

8. Ex. 5 Solve using matrices
y = -7
z = 2
(4, -7, 2)

9. Unique Solutions
Find detA. If it = 0 then there is an unique solution.
If detA = 0 then the system does not have a unique solution.

10. Determine whether each system has an unique solution.
20x + 5y = x – 5y = 125

11. Assignment
Pg odd