Matrix Calculator

Solve matrices step by step

This calculator will add, subtract, multiply, divide, and raise to power two matrices, with steps shown. It will also find the determinant, inverse, rref (reduced row echelon form), null space, rank, eigenvalues, and eigenvectors and will multiply the matrix by a scalar.

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If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

At the heart of a multitude of computations in mathematics, science, and engineering lies the matrix. This is a rectangular arrangement of elements structured into rows and columns. Mastery over matrices and the ability to proficiently handle their manipulations are critical skills in these domains. Our Matrix Calculator is designed precisely for this purpose. It assists you in performing a broad spectrum of matrix calculations, doing so with efficiency and precision.

How to Use the Matrix Calculator?

Enter the elements of your matrix or matrices into the given fields. Make sure to enter the numbers row by row, column by column.

• Select the operation

Choose the matrix operation you wish to perform from the dropdown menu.

• Click "Calculate"

Once you've input the data and chosen the operation, click the "Calculate" button. The calculator will then provide the resultant matrix or the answer to your operation.

• Interpret the Result

The resultant new matrix or the output of the operation will be displayed.

What Can You Do With Our Matrix Calculator?

• Matrix multiplication

Our matrix multiplication calculator is quick and straightforward, saving you time when multiplying matrices. All you need to do is input the matrices, and the calculator does the rest, providing you with the new matrix.

• Matrix addition, subtraction, and scalar multiplication

These fundamental matrix operations can be performed with ease. Simply input your matrices, select the operation, and voila, your result is ready in seconds.

• Determinant, rank, and matrix inverse

These advanced matrix calculations are made easy with our calculator. Input your matrix, and let the calculator do the complex computations for you.

• LU decomposition, QR factorization, and SVD

The matrix calculator can be used to decompose the given matrix into a product of "simpler" matrices, saving you the labor of manual calculation.

• System of linear equations

The matrix calculator can be used to solve or "help" solve systems of linear equations, saving you the labor of manual calculation.

What Is a Matrix in Math?

In mathematics, a matrix is essentially a grid of numbers placed in rows and columns. These numbers are known as elements. For example, a simple 2x2 matrix might look like this:

$$A=\left[\begin{array}{cc}1&2\\3&4\end{array}\right]$$

In this matrix $A$, "1," "2," "3," and "4" are the elements. The matrix has 2 rows and 2 columns, so we describe it as a 2x2 matrix.

A more complex 3x3 matrix could be:

$$B=\left[\begin{array}{ccc}2&7&1\\9&3&8\\6&4&5\end{array}\right]$$

Here, $B$ is a matrix with 3 rows and 3 columns, hence termed as a 3x3 matrix, and numbers from $1$ to $9$ are the elements of the matrix.

Matrices are extremely powerful mathematical tools used for various purposes, such as solving systems of linear equations, representing linear transformations, and handling graph data structures in computer science. They also find significant applications in other disciplines like physics, engineering, computer graphics, and statistics.

Why Choose Our Matrix Calculator?

• Ease of Use

Our Matrix Calculator is user-friendly and straightforward, designed with an intuitive interface that is simple to navigate, making complex matrix operations accessible to everyone.

• Versatility

The calculator is capable of performing a wide array of matrix operations, from basic matrix multiplication to more complex operations like calculating the determinant, rank, or inverse, and solving systems of linear equations.

• Accuracy

It ensures accurate and error-free results, which is crucial when dealing with complex calculations and large matrices.

• Time Efficiency

The Matrix Calculator significantly reduces the time needed to perform matrix calculations, freeing you from tedious manual computations.

FAQ

Does the Matrix Calculator support complex numbers?

Yes, the Matrix Calculator supports complex numbers and variables.

I encountered an error while using the Matrix Calculator. What should I do?

Please ensure you've correctly inputted your matrices and selected the right operation. If you're still facing issues, feel free to contact our support team.

How does the Matrix Calculator solve systems of linear equations?

Depending on the nature and complexity of the system, the calculator uses matrix methods such as Gaussian elimination or LU decomposition in order to solve or "help" solve systems of linear equations.