Maths Matrices: Overview, Questions, Preparation

Suppose Ram is visiting a fair with his children: Raman, John, and Durga. They bought 3 toys: Cars, Trucks, and Bikes, each in a different quantity.

The above table is a way to represent the data in the above word problem in mathematical form. Similarly, a Matrix is a method to display this data; this light green part of the table can be represented in a matrix.

 A = $\left[\begin{array}{ccc}\hfill 2\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 3\hfill \end{array}\right]$

According to the NCERT definition, “A matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or the entries of the matrix.”

The values/functions in the matrices are called elements, such as the number of toys in the above matrix are elements. The vertical line of elements is called a column, and the horizontal line of elements is called a row. The above example has 3 columns and 3 rows.

If a matrix has m rows and n columns, the matrix will be called a $m\times n$ matrix. The order of the matrix is $m\times n$ . The matrix of order $m\times n$  is displayed below.

In concise form, the Matrix is also represented as $A={\left[a_{ij}\right]}_{m\times n}$ , where $1\le i\le m$ , $1\le j\le n$ $i,j\in N$ .

The element in ${\left(i,j\right)}^{th}$ position is denoted as element, $a_{ij}$ where i represents row and j represents column.

There are various types of matrices based on different factors, including resultant, elements, and other properties. Read types of matrices below.

There are specific ways to perform basic mathematical operations like addition, subtraction, and multiplication of matrices. You can check important Matrix operations below:

• Addition of Matrices
• Subtraction of Matrices
• Multiplication of a Matrix by a Scalar
• Multiplication of Matrices

Read the detailed version of these operations of matrices below:

Matrices are added by the sum of each corresponding element. If there are two matrices A and B, such that, $A={\left[a_{ij}\right]}_{m\times n}$ and are $B={\left[b_{ij}\right]}_{m\times n}$ two matrices of the same order.

Sum of matrices A and B (adding each corresponding element):

$A+B={\left[a_{ij}+b_{ij}\right]}_{m\times n}$

If there are three different matrices A, B, and C of the same order. The properties of the addition of matrices are given below:

Note Points:

• Two matrices must be of the same order to be added or subtracted. The addition of matrices is only defined for the same order.
• For every matrix, there exists an additive inverse matrix $-A=\left[-a_{ij}\right]$ such that $A+\left(-A\right)=O=\left(-A\right)+A$ . Where $-A$ is the additive inverse of the matrix A.

The subtraction of matrices follows almost same set of rules as addition. If $A={\left[a_{ij}\right]}_{m\times n}$ and $B={\left[b_{ij}\right]}_{m\times n}$ are two matrices of the same order, then difference of matrices A and B will be: $A-B={\left[a_{ij}-b_{ij}\right]}_{m\times n}$ .

• Subtraction of matrices does not commutative and associative properties as addition.
• $A-B$ is a matrix obtained by subtracting the elements of B from the corresponding elements of A.