Basic Matrix Calculator
Result:
More Calculators
BMI Calculator GCD Calculator Centroid Calculator Discount Calculator Exponent Calculator Variance Calculator Derivative Calculator Percentage Calculator Surface Area Calculator Circumference Calculator Right Triangle Calculator Quadratic Equation Solver Random Number Generator Complex Number Calculator Linear Equation Calculator Simple Interest Calculator Inverse of Matrix Calculator Compound Interest Calculator Standard Deviation Calculator Matrix Determinant Calculator Pythagoras Theorem Calculator Matrix Multiplication CalculatorHow 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
1. Addition of matrices
\[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}, B= \begin{bmatrix} 3 & 4 & 5 \\ 6 & 8 & 9 \end{bmatrix} \] \[ A+B = \begin{bmatrix} 4 & 6 & 8 \\ 10 & 13 & 15 \end{bmatrix} \]2. Subtraction of matrices
\[ A=\begin{bmatrix} 3 & 4 & 5 \\ 7 & 8 & 9 \end{bmatrix}, B= \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \] \[ A - B =\begin{bmatrix} 2 & 2 & 2 \\ 3 & 3 & 3 \end{bmatrix} \]For calculating different operations on matrices using above basic matrix calculator, you have to first set the order of matrix, then enter the matrix and press confirm button, after that choose the operation, then you will get the resultant matrix in the Result section.
