How to determine the order of matrix?
If a matrix has m rows and n columns, its order is said to be m × n (read as ‘m by n’).
Examples:
[15 9 -5] is of order 1 × 3;
\(\begin{bmatrix} 7 & -6 \end{bmatrix}\) is of order 2 × 1;
\(\begin{bmatrix} a & b\\ c & d \end{bmatrix}\) is of order 2 × 2;
\(\begin{bmatrix} 8 & a & 5\\ -3 & 15 & b \end{bmatrix}\) is of order 2 × 3.
Clearly, a matrix of the order m × n has mn elements. Hence, if the number of elements in a matrix be prime, it must have one row or one column.
Usually, a matrix is denoted by a capital letter, such as A, B, C, D, M, N, X, Y, Z, etc.
Solved Examples on Order of a Matrix:
1. Let M = \(\begin{matrix} 5 & 4 & -3 & \\ 2 & -7 & 8 & \end{matrix}\).
What is the order of the matrix M?
Solution:
The order of the matrix A is 2 × 3 because there are 2 rows and 3 columns in the matrix.
2. If a matrix has six elements, find the possible orders of the matrix.
Solution:
6 = 1 × 6;
6 = 6 × 1;
6 = 2 × 3;
6 = 3 × 2
Therefore, the possible orders of the matrix are 6 = 1 × 6, 6 × 1, 2 × 3 and 3 × 2.
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