# 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:    2   by   3 Matrix 2:   3   by   2 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).