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Homework answers / question archive / MA129 Lab Report 4 - Systems of Linear Equations; Matrices Name: Winter 2021 1

MA129 Lab Report 4 - Systems of Linear Equations; Matrices

Name: Winter 2021

1. Suppose A =

5 |
-2 |

-2 |
1 |

-4 |
2 |

B =

3 |
4 |
-1 |

1 |
0 |
1 |

-3 |
0 |
2 |

And C =

0 |
-2 |

-1 |
1 |

0 |
1 |

If possible, determine each of the following.

(a) A-C (b) (A-—C)B (c) B(A-C)

2. Suppose that each of the following matrices represents a system of linear equations. Solve each system of equations.

You may assume the variables are x, y, and z in each system of equations.

(a) =

1 |
-13 |
-25 |
2 |

0 |
1 |
7 |
17 |

0 |
0 |
0 |
3 |

(b) =

1 |
2 |
-4 |
1 |

0 |
1 |
3 |
-2 |

0 |
0 |
0 |
0 |

(c) =

1 |
-7 |
2 |
12 |

0 |
1 |
3 |
-4 |

0 |
0 |
1 |
5 |

3. Solve the following system of equations using the method of substitution:

2s – 9t = 3

-5s + t = 14

4. 1550 tickets have been pre-sold for the production of Hamilton, in 2022. Box seats were $500, orchestra seats were $240, and balcony seats were $80. The total income from ticket sales was $273,000 and the combined number of orchestra and balcony seats was 30 times the number of box seats sold.

(a) Set up a system of three equations representing this situation. Make sure to clearly assign variables to each unknown quantity.

(b) Use matrices to determine how many seats of each type were sold. Continue using row operations until you have your matrix in row-echelon form. Include a concluding statement in your solution.