Basic Maths 2

Tutorial 5
Questions for in-class tutorial:
Basic Maths:

  1. Given the following matrices:

A = ,  B = , C =  , D = ,  E =

  1. a) Show that AB ≠ BA
  2. b) Determine the following if possible:

(i) AC     (ii) DC     (iv) A+B        (v) B+D

  1. c) Write down the transpose of D
  2. d) Evaluate the determinants: and
  3. Solve the following equations by Gauss-Jordan elimination:

2x + y + z = 12                           (1)
6x + 3y – 3z = 6                         (2)
4x – y + 5z = 6                           (3)
Application Question:

  1. A company with manufacturing plants located in Massachusetts (MA) and Virginia (VA) has labour-hour and wage requirements for the manufacture of three types of inflatable boats as given in the following two matrices.

 

Labour hours per boat
Cutting
department
Assembly
department
Packaging
department

 

Hourly wages
MA VA
  1. Find the labour costs for a one-person boat manufactured at the Massachusetts plant.
  2. Find the labour costs for a four-person boat manufactured at the Virginia plant.
  3. Discuss possible interpretations of the elements in the matrix products and .
  4. If either of the products or  has a meaningful interpretation, find the product and label its rows and columns.

Questions for self-study

  1. Evaluate each of the following determinants:
  2. a) b)
  3. Find the inverse of the matrix

A =  using the Gauss-Jordan elimination method. Use the inverse matrix to solve the following system of equations:
x – 2z = 2                            (1)
2x + 2y + 3z = 4                 (2)
x + 3y + 2z = 12                 (3)
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