## Introduction to Matrix Calculator

Today we will discuss the working of Matrix Calculator. Matrix math is actually a collection of elements, arranged in rows and columns and the combination of linear equation. In matrix math,

the numbers 1, 2, 3, 4,…..n

are called the entries or elements of the matrix. Matrix represented by the following symbols **()**,**[]**,**|| ||**,e.g.

$$\left[\begin{matrix} 2 & 1 & 3 \\ 4 & 2 & 1 \\ 3 & 3 & 2 \\ \end{matrix}\right] 3*3 $$

There are many types of a matrix for example; row matrix, column matrix, square matrix, null matrix, identity matrix, diagonal matrix, scalar matrix, triangular matrix, transpose matrix, symmetric matrix, skew matrix, equal matrix, algebraic matrix. Now we will know how matrix calculator performs its function.

No doubt, matrices have various applications not only in different branches of mathematics but also in physics, economics, engineering, statistics and economics. So, matrix equality calculator has it’s actual benefits nowadays.

Also find other math tools like the significant figures calculator & permutation calculator.

## How Matrix Calculator multiply matrices equations

Let us start to know the working of symmetric matrix calculator. First I will let you know about the sizes of each matrix because not every matrix can be multiplied by another matrix. So, let’s take a look at the size of this first matrix which has 2 rows and 3 columns and the second one matrix has 3 rows and 3 columns.

So the first matrix is a two by three matrix. If we take a look at the second matrix, it is three by three matrix. So, in order to multiply two matrices together the columns in the first matrices must equal the rows in the second matrix.

$$\left[\begin{matrix} 2 & 3 & 1 \\ 2 & -7 & 4 \\ \end{matrix}\right].\left[\begin{matrix} 3 & 4 & 5 \\ 1 & 1 & 4 \\ 2 & 1 & 4 \\ \end{matrix}\right]$$

These two inside numbers must be the same. If these two numbers are not the same, symmetric calculator can't multiply the two matrices. So, make sure about these numbers are the same, before multiply matrices. The outside numbers give you the size of the new matrix after you have done multiplication. Here outside numbers are 2 and 3, so the new matrix size will be 2 by 3 matrix.

Related: Use distance formula calculator & arithmetic sequence calculator for learning & practice regarding different math concepts.

Now let us take start, what actually we do when we multiply two matrices. We will multiply the rows of the first matrix by the columns of the second one.

$$\left[\begin{matrix} 2 & 3 & 1 \\ 2 & -7 & 4 \\ \end{matrix}\right].\left[\begin{matrix} 3 & 4 & 5 \\ 1 & 1 & 4 \\ 2 & 1 & 4 \\ \end{matrix}\right]$$

Also learn how to calculate sample covariance & ways to calculate average values online.

skew symmetric matrix calculator will multiply 2 of the first matrix to 3 of the 2nd matrix and so on. We highlighted them with the same color to make it easy to understand.

Matrix symmetric calculator will multiply the next columns with the same row.

After that, it apply multiplication to the 2nd row of first matrix with all columns of the 2nd matrix.

**Finally,**

$$=\left[\begin{matrix}11& 12& 26\\7&5&-2 \end{matrix}\right]$$

This is how skew symmetric matrix calculator works efficiently to compute results.

With your learning regarding matrix multiplication, you can also learn about the calculations of factor and how to calculate factorial using factorial calculator.

## Matrix Multiplication Calculator

In an A is a n*n matrix, I also a n*n matrix, in this situation the n*n matrix B. It will be denoted as B = A^{-1} and it will be said as an inverse matrix ( AA^{-1} = A^{-1} A = I). Inverse matrix is denoted by A^{-1}.

To obtain inverse matrix A for which A^{-1} exists, the matrix multiplication calculator do the following steps. First of all, form an augmented [ A/I] matrix in which I is an n*n identity matrix. Then, to get a matrix [I/B], perform row transformations on [ A / I]. Actually here, matrix B is A^{-1}. At last step, verify it by showing that these matrices are equal to each other e.g. B.A = A.B = I.

Related: Use other free tools of math like remainder calculator & z score calculator for practice and learning.

One thing must be noted that every matrix does not have inverses but only square matrices. It is not necessary that every matrix has an inverse. And it’s the special property of an inverse matrix that it is unique but if it exists. Any matrix has no more than one matrix.

Also try our trignometry calculators of slope calculator and cylinder volume calculator for more practice and learning the digital way of calculating complex equations.

## How to find the best Matrix Calculator?

There are a lot of matrix product calculator to find the matrix product. You'll find all those matrix solution calculator online but the key is to find the best one which compute matrix without any errors.

Calculatored has a ton of converters and calculators and matrix product calculator is one of those. You can use our symmetric matrix calculator free online as it provides accurate results.

Calculatored also offers a lot of tools which you can use like we have midpoint formula calculator and mean calculator.

## How to use Matrix Calculator?

Our matrix product calculator is the best calculator to solve a system of equations and it is not difficult to use it. You just need to follow those steps to calculate results. The steps for using matrix solution calculator are as follows:

Step #1: Enter the matrix values in Row 1

Step #2: Enter the 2nd matrix values in Row 2

Step #3: Select if you want to calculate Inverse matrix or 2*2 matrix

Step #4: Click on the find button

Instantly after clicking on the button our matrix solution calculator will instantly show you the accurate results. There are other useful online tools you can use on our portal like integral calculator and derivative calculator.