Have you ever played Sudoku? The picture on this page shows a 9 × 9 Sudoku puzzle. The goal is to fill each column, row, and the smaller 3 x 3 boxes with the digits 1 through 9. Since there are only 9 boxes in each, none of the digits can be repeated. This rectangular array of digits can be represented using a matrix. Matrices (matrices is the plural of matrix) are very useful for representing and solving problems in mathematics. In this lesson, you are going to explore matrices and use them to solve systems of equations.
Note: Remember to show all of the steps that you use to solve the problem. You can use the
comments field to explain your work. Your teacher will review each step of your response to
ensure you receive proper credit for your answer.
Given the system of constraints, name all vertices of the feasible region. Then find the
maximum value of the given objective function.
x>0
y 30
Constraints 1
vs-x + 3
3
5 2 y + x
Objective Function: C = 6x – 4y
8.
(3 points)
Solve the system by elimination.
I-2x + 2y + 3z 0
-2x – y + z = -3
(2x + 3y + 3z = 5
(3 points)
Note: Remember to show all of the steps that you use to solve the problem. You can use the
comments field to explain your work. Your teacher will review each step of your response to
ensure you receive proper credit for your answer.
Solve the system by substitution.
-x-y-z = -8
-4x + 4y + 5z 7
=
2x + 2z = 4
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