[Maths Class Notes] on Determine The Order of Matrix Pdf for Exam

Before we know what the order of a matrix means, let’s first understand what matrices are. Matrices can be defined as rectangular arrays of numbers or functions. Since a matrix is a rectangular array, it is 2-dimensional. A two-dimensional matrix consists of the number of rows which is denoted by (m) and a number of columns denoted by (n). Let us understand the concept in a better way with some examples.

What is a Matrix?

• A matrix is a rectangular array of numbers or symbols which are generally arranged in rows and columns.

• The order of the matrix is defined as the number of rows and columns.

• The entries are the numbers in the matrix and each number is known as an element.

• The plural of the matrix is matrices.

• The size of a matrix is referred to as the ‘n by m’ matrix and is written as m × n, where n is the number of rows and m is the number of columns.

• For example, we have a 3 × 2 matrix, that’s because the number of rows here is equal to 3 and the number of columns is equal to 2.

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How Will You Determine the Order of a Matrix?

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The order of a matrix can easily be determined by counting the number of rows and columns the matrix consists of. If we have a matrix that has m number of rows and n number of columns, then let’s know how to find the order of the matrix.

Here are a few examples of how to find the order of a matrix,

[7−6]‘ role=”presentation”>$\left[\begin{array}{cc}7& -6\end{array}\right]$

The order of the above matrix is (1×2) since the number of rows (m) = 1 and the number of columns (n) = 2.

[8a5−315b]‘ role=”presentation”>$\left[\begin{array}{ccc}8& a& 5\\ -3& 15& b\end{array}\right]$

The order of the above matrix is (2×3) since the number of rows (m) = 2 and the number of columns (n) = 3.

The order of the matrix below is 3 x 4, which means that it has 3 rows and 4 columns.

[8a5−315b]‘ role=”presentation”>$\left[\begin{array}{ccc}8& a& 5\\ -3& 15& b\end{array}\right]$

In the example given above, what is the order of a matrix? The matrix order math is 2 × 3. Therefore, the number of elements present in the above matrix will also be 2 times 3, which is equal to 6.

This gives us an important insight that if we know the order of the matrix, it would be easy for us to determine the total number of elements present in the matrix. In conclusion, if the order of the matrix is m × n, it will have mn (product of m and n) elements. 

Now, you might wonder whether the converse of the previous statement is true?

The converse of the previous statement s
ays that: If the number of elements is equal to mn, then the order would be m × n. But, this is definitely not true. This is because the product of mn can be obtained in more than one way; some of the ways are listed below:

•  mn × 1

• 1 × mn

• m × n

• n × m
  

What are the Different Types of Matrix?

There are different types of matrices. Here they are –

Example: [1234]4×1‘ role=”presentation”>${\left[\begin{array}{c}1\\ 2\\ 3\\ 4\end{array}\right]}_{4\times 1}$  

Example: [173242466913]‘ role=”presentation”>$\left[\begin{array}{cccc}1& 7& 3& 2\\ 4& 2& 4& 6\\ 6& 9& 1& 3\end{array}\right]$

Example: The below example is showing a 3×3 square matrix.

[000000000]‘ role=”presentation”>$\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$

Example: [400040004]‘ role=”presentation”>$\left[\begin{array}{ccc}4& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right]$

Example: [832046009]‘ role=”presentation”>$\left[\begin{array}{ccc}8& 3& 2\\ 0& 4& 6\\ 0& 0& 9\end{array}\right]$

Example: [123245356]‘ role=”presentation”>$\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& 5\\ 3& 5& 6\end{array}\right]$

• Anti-symmetric Matrix: Anti-symmetric matrix is a type of matrix which has negative values to its transpose A= – AT
  , i.e., amn = -anm. This type of matrix is also called a “skew-symmetric matrix”

Example: [349121113]‘ role=”presentation”>$\left[\begin{array}{ccc}3& 4& 9\\ 12& 11& 13\end{array}\right]$

Solution) The number of rows in the above matrix A = 2

The number of columns in the above matrix A= 3 .

Therefore, the order of the matrix is 2 × 3.