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SAT Problem Of the Day
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4.4 Solving Systems with Matrix Equations4.4 Solving Systems with Matrix Equations4.4 Solving Systems with Matrix Equations4.4 Solving Systems with Matrix Equations
Objectives: •Use matrices to solve systems of linear equations in mathematical and real-world situations
Let x represent the amount invested at 4%
x + y = 5000
Example 1Amy has saved $5000 during the past three summers. Now she wants to put some of the money into an investment that earns 4% per year and some into an investment that earns 11% per year. How much money should Amy invest at each interest rate to earn $500 in interest per year?
Step 1: Choose your variables
Let y represent the amount invested at 11%
Step 2: Write a system of equations
.04x + .11y = 500
Step 3: Write the system as a matrix equation, AX = B
1 1
.04 .11
x
y
5000
500
Step 4: Solve for the variable matrix, X, by finding the product A-1B
$714.29 at 4% and $4285.71 at 11%
Example 2Refer to the system of equations below.
a) Write the system as a matrix equation
b) Solve the matrix equation
3x 6y 4z 8
x 4y 2z 3
8y z 0
3 6 4
1 4 2
0 8 1
x
y
z
8
3
0
13 6 4
1 4 2
0 8 1
x
y
z
8
3
0
1.8
0.1
0.8
x = - 1.8 y = - 0.1 z = - 0.8
Example 3Refer to the system of equations below.
a) Write the system as a matrix equation
b) Solve the matrix equation
9x 3y 27
6x 2y 18
9 3
6 2
x
y
27
18
19 3
6 2
x
y
27
18
PracticeRefer to the system of equations below.
a) Write the system as a matrix equation
b) Solve the matrix equation
3x 4y 3
6x 8y 6
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