Question

What is scalar multiplication of matrices?

Answer 1

Simply the multiplication of a scalar (generally a real number) by a matrix.

The multiplication of a matriz `M` of entries `m_(ij)` by a scalar `a` is defined as the matrix of entries `a m_(ij)` and is denoted `aM`.

Example:

Take the matrix

`A=((3,14),(-4,2))`

and the scalar `b=4`

Then, the product `bA` of the scalar `b` and the matrix `A` is the matrix

`bA=((12,56),(-16,8))`

This operation has very simple properties that are analogous to that of the real numbers.