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About matrix multiplication calculator
This is a free online matrix multiplication calculator with complete, detailed, step-by-step description of solutions, that performs operations with matrices up to 99x99 in size with matrix elements of this type: decimal numbers, fractions, complex numbers, variables.
To start the calculation, you need to first enter the size of the matrix in the input field that you can find from the very top of the screen, also there you can choose the desired method of calculation.
A little below you will find a matrix window in which you need to enter matrix elements using the keyboard. The matrix control panel is also located here, which simplifies work with matrices and contains the following control elements:
- The first element allows you to expand the matrix window. This can be especially useful in cases where you need to perform calculations with very large matrices that do not fit completely. If the matrix is still not visible after expanding the window, you can change the scale of the matrix using the + / - buttons;
- The second element performs the function of copying the matrix input to the memory buffer. This can be useful in cases where you often use the same matrix for calculations, or if you need to move matrices between operations;
- And the last element inserts the previously copied matrix, which allows you to speed up the process of entering the matrix to just a few clicks, instead of doing it manually;
And further down you will find a toolbar that allows you to customize the calculator and make it easier to work with it. It is visually divided into three parts, each of which is responsible for the following functionality:
- The first allows you to select the number format when the solution result is displayed. Also, here you can turn off comments to the solution of the problem if you have already understood how to solve this problem, and you use the calculator to speed up or check your own calculations. Or you can turn off the step-by-step solution entirely if you only need the result of the solution;
- The second contains buttons that allow you to change the type of the matrix input field, erase its elements or the entire matrix, and the largest button with an equal sign, which will take you to the screen with the solution of the problem. All these buttons are duplicated by keys on the keyboard. To find out which key on the keyboard to press, simply hover over one of the buttons and a tooltip will appear with the name of the key. You can also use the arrow keys on your keyboard to move the cursor between matrix input fields;
- And the last one allows you to choose the number of digits after the decimal point for rounding non-integer numbers. Also, here you can immediately see an example of how rounded fractions will look;
What is matrix multiplication?
Matrix multiplication is the operation of multiplying one n x m matrix by another m x k matrix, resulting in a new third n x k matrix called the product of these two matrices. Multiplication of two matrices is possible only if the number of columns in the first matrix is equal to the number of rows in the second matrix. The matrix obtained as a result of the multiplication of two matrices will have the same number of rows as in the first matrix and the same number of columns as in the second matrix.
How to multiply two matrices?
To multiply two matrices, you need to do the scalar product of each row of the first matrix by each column of the second matrix. The scalar product is an operation during which you need to multiply each element of the row of the first matrix by the corresponding element of the column of the second matrix, then you need to add up all the products to get one single number that is an element of the resulting matrix. So, to find, for example, the first element of the resulting matrix when multiplying two matrices, you need to scalar multiply the first row of the first matrix by the first column of the second matrix.
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