Matrix-Vector Product

Next, or the right arrow key, steps through the product:

1. $\overline{x}$ is split into its components, each a scalar.
2. Each column of $A$ is multiplied by its scalar.
3. The scaled columns are added to give $A\overline{x}$.

The left arrow key steps back. Every entry can be edited. $A$ can have up to four rows and four columns, and $\overline{x}$ up to four components. When the number of columns of $A$ differs from the number of components of $\overline{x}$, the product is marked undefined. In the last step, the column or component with no partner is marked. Abstract m × n runs the same steps with entries $a_{ij}$ and $x_j$ for a general $m \times n$ matrix.