### What is the Matrix?

Matrix is a set of numbers or characters arranged in rows and columns that generally forms a square or rectangle. The unit of a matrix is denoted as elements. They can perform mathematical functions like addition, subtraction, multiplication, division, and many more. Matrix is enclosed within square brackets. Matrix is an integral part of linear algebra.

 a b c d

#### What is a determinant?

In Linear algebra, a determinant is a numerical value for a square matrix. Every square matrix can be denoted by one number, which is known as a Determinant. It is generally denoted as |A| or det A.

A determinant enciphers some properties of the matrix. The square matrices with determinant non zero can be inverted. The determinant is used to solve linear equations, calculus, and a lot more.

#### Determinants' properties

1. Even if the column and rows interchange, the determinant remains unchanged.
2. The Sign changes (+ will change to – and vice versa) when two columns or rows are interchanged.
3. If a determinant's two rows or columns are the same, then the determinant is 0.
4. The determinant is 0 if two columns and rows are identical.
5. When a matrix is multiplied with a variable f the determinant value should be multiplied by the f value.

Calculation of determinant in 2 x2 matrix is |A|= ad – bc

For example,

 2 3 4 5

|A| = (2 x 5) -(3 x 4) = 10 -12 = -2

The determinant of the given matrix is -2.

The calculation of sizes above 2 x 2 is computed differently.

#### Gaussian Elimination Method

By using the Gauss method, you can transform the square matrix in such a way that the lower triangle of the matrix becomes zero. This is possible by using the rules of row-factor and addition.

The online calculator also computes the value of (N x N matrix) determinant by using the Gaussian algorithm and further it shows all the detailed calculation steps in echelon form.

• Transformation of the determinant
 2 4 8 3 1 7 6 5 9
• Division Of Rows 1 To 3 By The Element Of The Row In The Column 1
36  1 2 4 1 0 2 1 1 2
• Subtracting The 1. Line of The Following
36  1 2 4 0 -2 -2 0 -1 -3
• Division of Rows 2 To 3 By the Element Of The Row In The Column 2
70  1 2 4 0 1 1 0 1 2
• Subtracting The 2. Line of The Following
70  1 2 4 0 1 1 0 0 1
• Division of rows 3 to 3 by the element of the row in the column 3
80  1 2 4 0 1 1 0 0 1

The Value of The Determinant Is:

det(A)=80

#### Functions of matrix determinant calculator

The determinant calculator 3x3 is normally used in solving Mathematical problems. It is a proven aid for Students to verify their answers. There are several features which make the determinant of 3x3 matrix calculator convenient. Here are some,

• Determinant of a matrix calculator is on an Online platform, which makes it compatible for a wide range of devices.
• Deliberates a prompt response: In blink of one’s eye the entire answer is displayed on screen.
• The Interface is Highly Interactive: Solving a determinant problem may be confusing but matrix determinant calculator is very easy to use.
• The Complete Step by Step method is displayed on screen: The Entire solution of linear algebra is solved using Gauss Method.
• It facilitates N x N matrix: it supports matrix with size larger than 5 x 5

#### How to find the determinant of a 3x3 matrix using a calculator?

The operation of the matrix determinant Calculator uses Smart Algorithms and functions very fast. The determinant of a matrix calculator is error free.

The steps to find determinant of 3x3 matrix using calculator are as follows:

1. Firstly, set the size of the matrix. It may be of size 2 x 2, 3 x 3, 4 x 4 and up to N x N.
2. Enter the values in the matrix simply by typing or using scroll buttons. Any integer numbers (-3, -2, -1, 0, 1, 2, 3) can be used in calculations.
3. After entering the elements of the matrix, click on “Calculate”.
4. The Solution will be displayed instantly on the screen. The answer involves a detailed step by step solution and determinant of a matrix calculator at the end.
5. For fresh operation click on the “clear” option.