1. Lesson 8: Solving Systems of Equations with Matrices
Accel Precalc
Unit 3: Matrices
Lesson 8: Solving Systems of Equations with Matrices
EQ: How do you use matrices in the graphing calculator to solve systems of equations?

2. How do you enter matrices in your graphing calculator?

3. Enter the remaining matrices in your
calculator.

5. What does this mean in terms of the matrices?

8. A system of equations may be represented as a matrix equation
A system of equations may be represented as a matrix equation. For example, the system of equations
may be represented by the matrix equation

9. Ex. 1 Write the matrix equation that represents the system:

10. Ex. 2 Write the matrix equation that represents the system:

11. Ex. 3 Write the system of equations represented by the matrix equation

12. Day 32 Agenda:

13. A matrix equation is in the form AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

14. Solving AX=B Real Numbers ax=b (1/a)(ax) = (1/a)b (1/a)(a)x = b/a
Note: 1/a must exist to solve ax = b

15. Solving AX=B Real Numbers ax=b (1/a)(ax) = (1/a)b (1/a)(a)x = b/a
Matrices
AX=B
A-1(AX)=A-1B
(A-1A)X=A-1B
IX=A-1B
X=A-1B
Note: A-1 must exist to solve AX=B

16. How do you use matrices to solve systems of equations?
Refer back to Ex 1. Solve the system of equations using a matric equation.
x = -7
y = 15

17. Ex 4 Solve the system of equations using matrices.

18. Ex. 5 Solve the system of equations using matrices.
z = 5

19. In Class Practice: Set up the correct matrix equation then solve.

21. Let x = amount invested at 5% Let y = amount invested at 14%
Ex. 6 Application
A financial manager wants to invest $50,000 for a client by putting some of the money in a low-risk investment that earns 5% per year and some of the money in a high-risk investment that earns 14% per year. How much money should she invest at each interest rate to earn $5000 in interest per year?
Let x = amount invested at 5% Let y = amount invested at 14%
x + y = 50000
.05x + .14y = 5000

22. Write as a matrix equation to solve.

24. YES!!! Multiplication of matrices DOES NOT follow the commutative property.

25. x + y = 50000
.05x + .14y = 5000
Write as a matrix equation to solve.
She should invest $22, at 5% and $27, at 14% to earn $5,000 per year.

26. Ex 7 Solve the system using a matrix equation.
Matrix A does not have an inverse. (What is the determinant of A?) Determine if the system is inconsistent or dependent.
This system is inconsistent (parallel lines) because the slopes are the same but the y-intercepts are different.

27. Ex. 8 Solve the system using a matrix equation.
Matrix A does not have an inverse. (What is the determinant of A?) Determine if the system is inconsistent or dependent.
This system is dependent (same line) because the slopes are the same and the y-intercepts are the same.

28. Assignment:
Textbook p #51 – 63 odd
Use a matrix equation to solve each system. If there is not a unique solution, classify the system as consistent dependent or inconsistent.