Leading diagonal (major diagonal)

This is a line of numbers that runs diagonally from the top left-hand corner to the bottom right-hand corner for the

matrix with equal numbers of rows and columns (i.e. a square matrix). Consider the matrix below.

image 34

This matrix has the same number of rows and columns. It is a 3 3 matrix. Its leading diagonal is what has been enclosed in the loop below.

image 35
  1. Minor diagonal
    This is a line of numbers that runs diagonally from the bottom lefthand corner to the top right-hand corner. For the matrix above its minor diagonal is what has been enclosed in the loop.
image 36

1, 5 and 3 are the entries of the minor diagonal.

Types of matrices

  1. Column matrix
    This is a matrix with only one column. E.g.
image 37

2. Row matrix
This is a matrix with only one row. E.g. c = (0 ,4)

  1. Zero matrix
    This is a matrix whose all of its elements are zeros. E.g.
image 38
  1. Equal matrix
    Two or more matrices are equal if and only if their corresponding elements are equal and are of same order.
    Example.

Given

image 39

is equal to mattrix B, then

a =4, b= 10

c =6 , d=-4

  1. Square matrix
    This is a matrix with equal number of rows and columns. E.g.
image 40
  1. Identity matrix
    This is a square matrix with 1 as an element in the leading (major) diagonal and zeros elsewhere. At times, it is known as unit matrix and it is denoted by the letter I. Some few examples of identity matrix include the following:
image 41

Example

  1. Three sales girls sold the following number of bottles of lotion on a certain day.
    Liz sold 9 bottles of Dear heart, 13 of Razac and 6 of Venus.
    Suzi sold 8 bottles of Movit lotion, 7 of Razac and 10 of Venus.
    Aber sold 15 bottles of Movit lotion, 1 of Dear heart and 18 of Razac.
    Show this information in a 3×4 matrix.
    Solution
image 42
  1. The table below shows the number of times that three couples attended various types of entertainment in one year.
image 43

a) Write down the information in the table in the form of a matrix and state the order of the matrix

b) Write the Frank’s attendance as a column matrix. What is the order ofthis matrix?

c) Write as a row matrix, the number of times the plays have been attended, and state the order of the matrix.

image 44

c = (8,1) = The order is 1 X 3