Matrices is the plural of a matrix. A matrix is a rectangular array of numbers whose value and position in the arrangement is significant.
It is common to store large quantities of data and numerical information in form of tables.
converting tables to matrices
The table below shows marks scored by three students in an exam.
| Name | Mathematics | Physics | chemistry |
|---|---|---|---|
| Jane | 40 | 59 | 48 |
| Phyllis | 56 | 63 | 65 |
| James | 78 | 81 | 71 |
the data can be written as matrices form as :
consider the table below that shows English soccer results. A win scores 3 points, draw 1 point while loss wins zero points.
| Team | matches played | wins | Draws | loses | Goals | points |
|---|---|---|---|---|---|---|
| Arsenal | 25 | 18 | 5 | 2 | 49 | 59 |
| Man city | 25 | 15 | 5 | 5 | 51 | 50 |
| Aston Villa | 25 | 14 | 5 | 6 | 36 | 47 |
| Man U | 24 | 13 | 6 | 5 | 46 | 45 |
| chelsea | 23 | 12 | 5 | 6 | 45 | 41 |
| Liverpool | 23 | 11 | 7 | 5 | 40 | 40 |
| Brentford | 22 | 11 | 8 | 3 | 39 | 41 |
| Sunderland | 22 | 10 | 9 | 3 | 27 | 39 |
| Fullham | 21 | 9 | 4 | 8 | 35 | 31 |
| Newcastle | 19 | 8 | 5 | 5 | 35 | 29 |
with time, we may get to know what each team is scoring and remember each column values. In that case, we only need to remember the patterns only. The numerical data will thus be presented in form of a matrix as shown.
We have just converted a table to a matrix
A matix is represented as a brackets or square brackets as shown:
Capital letters in bold are commonly used to denote a matrix.
Each number in a matrix is referred to as an element of a matrix.
Order of matrices
Matrix size and shape depends on the number of rows and columns it has. If the number of rows equals number of columns, then it is a square matrix, otherwise it is a rectangular matrix. A matrix has rows and columns.
Rows are the horizontal arrangement of items while columns are the vertical arrangement.
Order of a matrix
A matrix with m rows and n columns is said to be a matrix of order m x n .
The order of matrix denotes the number of rows and columns in the matrix.
Therefore, a matrix of order 4 x 3 will have 4 rows and 3 columns.
A matrix of order 1 x n is called a row matrix.
A matrix of order m x 1 is said to be a column matrix.
A square matrix is a matrix of order m x m or n x n.
The matrix below is a square matrix of order 4 x 4:
elements of a matrix
Each number or item in a matrix is called an element of the matrix. Each element can be located in the matrix by stating it’s position in the row or column.
Position of an element in a matrix is described by use of suffices.
If A is a matrix and am,n is an element in that matrix, then am,n is the element in the mth row and on the nth column.
consider the matrix above, 1 is an element at a3,3 position.
As an example, consider the matrix:
generally, element aij means an element in the ith row and jth column.
A matrix where all the elements are zero is known as Zero or null matrix.
We denote matrices by a capital letter in bold face. For example:
summary
practice exercise on matrices
- The table below shows marked scored in three tests by grade 10 students.
| Student | Test 1 | Test 2 | Test 3 |
|---|---|---|---|
| Jane | 68 | 73 | 56 |
| Milliam | 79 | 71 | 67 |
| Nancy | 67 | 59 | 63 |
| James | 45 | 56 | 78 |
| Mark | 62 | 70 | 86 |
| Eliud | 71 | 74 | 82 |
| Brian | 89 | 84 | 87 |
| Harriet | 84 | 76 | 77 |
(a) Write down the information from the table into a matrix and state order of the matrix.
(b) Write test 2 as a column matrix and state it’s order
(c) write as a matrix, Brian’s scores in the three test
(d) change the marks in test 1 and test to to 60% of the current value.
(e) convert test 3 to 40% of the current value.
(f) make a new matrix by adding a fourth column in the matrix above with the totals of (d) and (e) above
2. Given matrix A below. state the elements in:
(a) a1,3 (b) a2,4 (c) a3,2 (d)a4,1
Related topics
Databases
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