What the Desmos matrix calculator does

The Desmos matrix calculator lets you perform operations on matrices directly in your browser without installing software. You can add, subtract, and multiply matrices, find determinants and inverses, and transpose matrices. The tool displays your work step-by-step, so you can see how each operation is performed rather than just getting a final answer.

Desmos is a free graphing calculator platform that includes a dedicated matrix mode alongside its standard graphing tools. You access the matrix calculator by opening Desmos in any web browser, switching to matrix mode, and entering your matrices using the built-in grid interface.

Key Takeaways

  • Open Desmos in your browser, click the menu icon, and select "Matrix Calculator" to switch from graphing mode to matrix mode.
  • Enter matrix values by clicking cells in the grid and typing numbers; use Tab to move between cells and create new rows or columns as needed.
  • Perform operations by typing expressions like A + B, A * B, or det(A) in the expression line, where A and B are your matrix names.
  • Desmos shows you the result and displays intermediate steps for multiplication and other complex operations so you understand how the answer was calculated.

Opening the matrix calculator in Desmos

Go to desmos.com in your web browser. You do not need to create an account to use the calculator, though you can save your work if you sign in. Once the page loads, you will see the standard graphing interface with a blank coordinate plane.

Click the menu icon (three horizontal lines) in the upper left corner. A dropdown menu appears. Select "Matrix Calculator" from the list. The interface switches to matrix mode, and you will now see a grid where you can enter matrix values instead of a coordinate plane.

Entering your first matrix

In matrix mode, you see a grid labeled with a letter (usually A) on the left side. Click any cell in the grid to start entering numbers. Type your first value and press Tab to move to the next cell to the right. Press Enter to move down to the next row.

If you need more rows or columns than the grid currently shows, keep pressing Tab or Enter and Desmos will add them automatically. For example, to enter a 2×3 matrix (2 rows, 3 columns), click the first cell, type your first number, press Tab, type the second number, press Tab again, type the third number, then press Enter to move to row 2 and repeat.

Once you finish entering all values for matrix A, click below the grid or press the down arrow key. A new matrix grid labeled B appears. Enter your second matrix the same way. You can create as many matrices as you need by continuing this process.

Performing basic matrix operations

After entering your matrices, look for the expression line at the bottom of the screen (or in the left sidebar, depending on your screen size). This is where you type the operations you want to perform. Click in this line and type your expression using the matrix names and operation symbols.

To add two matrices, type A + B and press Enter. To subtract, type A - B. To multiply matrices, type A * B (note: matrix multiplication is not commutative, so A * B does not equal B * A). Desmos calculates the result and displays it in a new matrix grid below your expression.

For operations that work on a single matrix, type the function name followed by the matrix in parentheses. Type det(A) to find the determinant of matrix A. Type A^-1 to find the inverse of matrix A (if it exists). Type transpose(A) or A^T to flip rows and columns.

Understanding the step-by-step display

When you perform a multiplication or other complex operation, Desmos does not just show you the final answer. Click on the result matrix, and the calculator displays the intermediate steps used to calculate each cell. This is especially useful for learning how matrix multiplication works, since you can see which row and column were multiplied together to produce each result.

For example, if you multiply a 2×2 matrix by another 2×2 matrix, clicking the result shows you the dot products calculated for each position in the answer. This breakdown helps you verify your work or understand where an error occurred if the result is unexpected.

Working with multiple operations in one expression

You can combine operations in a single expression just as you would in algebra. Type (A + B) * C to add matrices A and B first, then multiply the result by matrix C. Use parentheses to control the order of operations. Desmos follows standard mathematical order of operations (multiplication before addition), so A + B * C multiplies B and C first, then adds A to the result.

You can also store intermediate results by assigning them to new matrix names. Type D = A + B to create a new matrix D that contains the sum of A and B. Then use D in later expressions, such as D * C or det(D).

Clearing matrices and starting over

To delete a matrix, click the matrix label (A, B, C, etc.) and press Delete or Backspace. The entire matrix grid disappears. To clear all your work and start fresh, click the menu icon and select "Clear All" or reload the page.

If you want to keep your work, click the menu icon and select "Save" (you will need to sign in to your Desmos account). Your matrices and expressions are stored in your account and you can return to them later by opening your saved file.

Frequently Asked Questions

Can I use the Desmos matrix calculator on my phone?

Yes. The Desmos website works on mobile browsers, though the interface is more compact. Matrix entry is slower on a phone because the grid is smaller, but all operations function the same way. For extensive matrix work, a desktop or tablet is more practical.

What happens if I try to multiply matrices with incompatible dimensions?

Desmos displays an error message explaining that the dimensions do not match. Matrix multiplication requires the number of columns in the first matrix to equal the number of rows in the second matrix. Check your matrix sizes and reorder your expression or adjust your matrices.

Can I find the rank or eigenvalues of a matrix in Desmos?

The Desmos matrix calculator supports basic operations: addition, subtraction, multiplication, determinant, inverse, and transpose. It does not calculate rank or eigenvalues. For those operations, you would need a more advanced tool like MATLAB, Python with NumPy, or Wolfram Alpha.

How do I know if a matrix has an inverse?

A matrix has an inverse only if it is square (same number of rows and columns) and its determinant is not zero. Type det(A) to check. If the determinant is 0, the matrix is singular and has no inverse. If you try A^-1 on a singular matrix, Desmos displays an error.

Can I import matrices from a spreadsheet or file?

No. You must enter matrix values manually using the grid interface in Desmos. There is no import feature. If you have a large matrix, typing each value takes time, but copying and pasting is not supported in the matrix calculator.