Matrix Calculator Multiplication

Multiplication of Matrices

A step by step matrix calculator multiplication is presented. It has been designed so that the steps needed to do mulitplications of rows of matrix 1 by the columns of matrix 2 are shown. Let \( M_1 \) be a matrix of dimensions \( m \times p \) and \( M_2 \) be a matrix of dimensions \( p \times n \), the mulriplication of \( M_1 \) and \( M_2 \) is given by \[ M_1 \cdot M_2 = M \] where \( M \) is a matrix of dimensions \( m \times n \)
In the calculator below, the elements matrices \( M_1 \) and \( M_2 \) are generated randomly and the mutliplication is done step by step for educational purposes.
The multiplication is done by multiplying the rows of \( M_1 \) by the columns of \( M_2 \) as shown in the steps of multiplication. At each step is shown the element \( M_{i,j} \) and the row (in red) mutliplied by the column (in blue).

Use of the Calculator for Matrix Multiplication

1) Enter matrices dimensions such that the number of columns of matrix 1 is equal to the number of rows of matrix 2. The default values already in the inputs may be changed.

Matrix 1:      by  
Matrix 2:     by  

2) Click "Generate Matrices" to generate matrices with random values of the elements. Then click on "Go Step by Step" to go through the calculations of all elements of the matrix \( M \) given by multiplicatiion.
Finally, click on "Show Answer" to view the matrix given by multiplication.
3) At each step is shown the the elements \( M_{i,j} \) being calculated and how it is calculated multiplying a row of matrix 1 (in red) by a column of matrix 2 (in blue).