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Matrices are a powerful mathematical tool used in various fields like engineering, physics, computer science, and more. In this tutorial, we will walk you through the fundamental concepts of matrices and showcase our suite of calculators that will assist you in solving matrix-related problems. You can also access our Math Tutorials and Math Calculators from the quick links below.

Matrices are an incredibly versatile and essential mathematical tool. Whether you're solving systems of equations, performing geometric transformations, or analyzing data, matrices come in handy. Our calculator suite is designed to facilitate and enhance your matrix-related endeavors, let's take a look at the calculators we provide to help you master the matrix:

- 1x1 Matrix Division Calculator
- 1x1 Matrix Multiplication Calculator
- 2x2 Eigenvalues and Eigenvectors Calculator
- 2x2 Matrix Division Calculator
- 2x2 Matrix Inverse Calculator
- 2x2 Multiplication Matrix Calculator
- 3x3 Matrix Division Calculator
- 3x3 Matrix Inverse Calculator
- 4x4 Matrix Inverse Calculator
- Companion Matrix Calculator

There is a certain number of rows and columns in a matrix. We can also say that a rectangular array defines a matrix. The number of rows and columns in a matrix may be similar or different but in both cases, the calculations related to them is quite difficult. This is why using a matrix calculator becomes necessary, especially for people who have to do these calculations on a daily basis. The Matrix Calculators are also useful for students who may wish to check their homework of validate that the way they are working out there matrix calculations is correct.

There are numerous terms included in a matrix calculator. We are aware of the simple calculators that help us perform basic calculations such as addition, division, multiplication, etc. With the rapid growth in technology, iCalculator has produced advanced math calculators including scientific calculators, graphics calculators, etc. These math calculators support the need for online calculators that help people perform higher-level mathematical problems like finding the inverse of a matrix, the Rank of a matrix, multiplication of two matrices, etc. To help people who are looking online for these calculators, we have made these matrix calculators that can solve higher-level mathematical problems related to the matrices in the blink of an eye.

Let's begin with some of the general terms related to a matrix.

A matrix may be defined as a rectangular array of numbers that are arranged into rows and columns (much like a spreadsheet). In statistics, we use matrix algebra to express collections of raw data or information.

Here are some of the common and general terms you will come across while dealing with matrices-

Elements are the numbers that appear inside a matrix are termed as the elements of the matrix.

Dimensions may also be termed as the "order" of the matrix. Dimensions tell us how many columns and rows a matrix has. For example, a 3 x 4 matrix means 3 rows and 4 columns (rows are listed first, followed by the columns).

A scalar is any real number

An Identity matrix is a matrix with zeros as elements and ones as diagonals is termed as an identity matrix.

Here is an example of an identity matrix

When we want to find out the solutions of the systems of linear equations or finding the inverse of a matrix, the determinant of a matrix comes into the play which is nothing but a set of special numbers. Some of the properties of a determinant are:

- The determinant of a matrix is a real number and it may contain negative numbers too.
- The inverse of a matrix exists only if the determinant of that matrix is a non-zero number.
- Determinants only exist for a square matrix.

The formula for calculating the determinant of a matrix may vary because it depends on the order of the matrix.

The symbol for the determinant of a matrix A is given by |A|.

The dimension of a matrix is nothing but the order of that matrix. If we want to subtract or add two matrices, the dimensions of both the matrices must be the same i.e., a matrix having 3 rows and 4 columns can be added or subtracted to another matrix having 3 rows and 4 columns. We cannot add or subtract a matrix of 4 x 3 dimension with another of 5 x 2 dimension.

A square matrix may be defined as a matrix having an equal number of rows and columns. We can also say that a matrix of order m x n is a square matrix if m=n. The matrices that are not square matrix are termed as rectangular matrices.

A singular matrix is a square matrix but all the square matrices are not singular.

You can tell by looking at any matrix whether it is singular or not. If one row or column of a matrix has its elements as zeros or two rows or columns of a matrix are identical, then the matrix is said to be a singular matrix. In this case, the determinant of a singular matrix is 0.

Some of the properties of a singular matrix are stated below:

- A singular matrix is always a square matrix.
- The determinant of a singular matrix is always 0.
- We cannot find the inverse of a singular matrix because the determinant of a singular matrix is 0.

You can check whether you can find the inverse of a particular matrix or not just by checking whether it is singular or not by finding its determinant.

It's great to have a regular calculator, but people who study math's or perform regular matrix calculations will find the online matrix calculator particularly useful and time saving. Particularly when working with complex matrix formula. When you encounter lengthy, difficult and time taking problems, you can use this matrix calculator and save your time by avoiding manual calculations. Why waste time with manual matrix calculations when you can easily calculate the math with the help of this good calculator.