# Basic Matrix Calculator

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## How To Use Basic Matrix Calculator

Lets first understand, what is a matrix and how we can perform operations on matrices?

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.

A matrix having m rows and n columns is called a matrix of order m × n or simply m × n matrix (read as an m by n matrix).

We denote matrices by capital letters. Some examples of matrices:

$A=\begin{bmatrix} a & b & c \\ d & e & f\end{bmatrix},B=\begin{bmatrix} g & h \\ i & j \\ k & l \end{bmatrix}$ $C \begin{bmatrix} m & n & o \\ p & q & r \\ s & t & u \end{bmatrix}$

Types of Matrices

1. Column matrix

A matrix is said to be a column matrix if it has only one column.

$X=\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$

2. Row matrix

A matrix is said to be a row matrix if it has only one row.

$Y=\begin{bmatrix} 4 & 5 & 6 \end{bmatrix}$

3. Square matrix

A matrix in which the number of rows are equal to the number of columns, is said to be a square matrix.

$Z= \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$

4. Diagonal matrix

A square matrix is said to be a diagonal matrix if all its non diagonal elements are zero.

$P=\begin{bmatrix} 1 \end{bmatrix},Q=\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$ $R= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}$

5. Scalar matrix

A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal.

$P=\begin{bmatrix} 6 \end{bmatrix},Q=\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}$ $R= \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}$

6. Identity matrix

A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an identity matrix.

$I_{1}=\begin{bmatrix} 1 \end{bmatrix},I_{2}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ $I_{3}= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

7. Zero matrix

A matrix is said to be zero matrix or null matrix if all its elements are zero. We denote zero matrix by O.

$O_{1}=\begin{bmatrix} 0 \end{bmatrix},O_{2}=\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$ $O_{3}= \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$

8. Ones matrix

A matrix is said to be ones matrix if all its elements are one.

$A= \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}$

Operations on Matrices

$A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}, B= \begin{bmatrix} 3 & 4 & 5 \\ 6 & 8 & 9 \end{bmatrix}$ $A+B = \begin{bmatrix} 4 & 6 & 8 \\ 10 & 13 & 15 \end{bmatrix}$
$A=\begin{bmatrix} 3 & 4 & 5 \\ 7 & 8 & 9 \end{bmatrix}, B= \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}$ $A - B =\begin{bmatrix} 2 & 2 & 2 \\ 3 & 3 & 3 \end{bmatrix}$