Introduction to the Rank of Matrix Calculator:
Rank of matrix calculator is an online tool that helps you to evaluate the rank of rows and columns from the given matrix. Our tool helps you to find rank of matrix using different methods that give the best suitable result for the given matrices.
The matrix rank calculator is a handy tool that helps you to get the solution of the system of linear equations to find the rank of the matrix quickly or easily.
What is the Rank of a Matrix?
The rank of the matrix is a process in linear algebra that helps you to know the matrix's dimension from the system of linear equations. It also tells the maximum number of rows and columns that are linearly independent.
The rank provides you with crucial information about the matrix's properties, such as invertible and the dimension of its column space and row space spanning.
How to Find the Rank of a Matrix?
There are different methods used to find rank of matrix but you need to know about the basis of the matrix. These methods are minor or echelon forms.
Let's see how the rank of a matrix calculator uses both methods to perform the rank of the matrices calculations. We can understand this with the help of an example.
How to Calculate the Rank of a 3x3 Matrix?
Suppose a 3 by 3 matrix to find the rank.
$$ A \;=\; \left[ \begin{matrix} 1 & 2 & 1 \\ -2 & -3 & 1 \\ 3 & 5 & 0 \\ \end{matrix} \right] $$
Solution:
To find the rank of the given matrix, the rank of matrix calculator uses the echelon form method in which row operation is used to solve the given matrix in simplest form.
Step 1:
First, check whether the first row leading entity is 1 or not. If not then make the entity into 1. In this matrix, the leading entity of the first row is 1 so we proceed to the next step.
Step 2:
Multiply 2 with R1 and then add with R2 to make zero at the bottom leading entity of the first row and 1 value in the second row.
Step 3:
Again, multiply R1 with 3 then subtract R3 from R1 to make the first value of the third row zero.
$$ R_2: R_2 + 2R_1 $$
$$ R_3: R_3 - 3R_1 $$
$$ A \;=\; \left[ \begin{matrix} 1 & 2 & 1 \\ 0 & 1 & 3 \\ 0 & -1 & -3 \\ \end{matrix} \right] $$
Step 4:
R3 is added with R2.
$$ R_3: R_3 + R_2 $$
$$ A \;=\; \left[ \begin{matrix} 1 & 2 & 1 \\ 0 & 1 & 3 \\ 0 & 0 & 0 \\ \end{matrix} \right] $$
Step 5:
To find the number of rows subtract a total number of rows n from the remaining number of rows.
$$ R \;=\; n - r $$
$$ R \;=\; 3 - 1 \;=\; 2 $$
Therefore the rank of the matrix is 2.
How to Use Rank of Matrix Calculator?
The matrix rank calculator has a simple interface that helps you to solve the given system of linear equations. You just need to put your equation in this calculator and it will give you results immediately. These steps are
- Select the order of the matrix from the given list of the rank of a matrix calculator or as per your problem of the matrix to find the rank.
- Enter the element of your matrix in the input field for solving the rank of the given equation.
- Check your given input equation value before clicking the calculate button to get the result of rank of the matrix.
- Click the “Calculate” button for the solution of the Rank of matrix method problems.
- Click the “Recalculate” button for the evaluation of more examples of the linear equation to check the rank.
Results from Matrix Rank Calculator:
Rank of matrix Calculator provides you with a solution to linear equation questions when you click on the calculate button. It may include as:
- In the Result Box:
When you click on the result button of the rank calculator matrix you get the rank value of the given matrix problem using the elimination method.
- Possible Steps Box:
Click on the steps option so that you get the solution of the rank or dimension of the matrix.
Advantages of Rank of a Matrix Calculator?
The rank calculator matrix has many advantages that you get when you use it to evaluate the given equation and get the rank of the matrix in a solution easily. These advantages are
- The matrix range calculator is a trustworthy tool that always provides you with an accurate ranking of the matrix in the solution.
- It is a speedy tool that find rank of matrix problems with solutions in a few second.
- The matrix rank calculator is a learning tool that helps you to enhance your learning about the rank of the matrix concept without going to any teacher.
- It is a handy tool that solves the rank of matrix problems with various methods without any external effort.
- Rank of matrix calculator is a free tool that allows you to use it for the calculation without charging a fee.
