Scalar Multiplication of MatricesReference > Mathematics > Algebra > Matrices
In this section, you will learn a new vocabulary word. The word is scalar. If you look up definitions of scalar, you might see scary things like this:
- A non-vector quantity
- A quantity having magnitude, but not direction
- The real component of a quarternion
- The reduction of a vector, matrix or tensor to a single component
If these definitions scare you, don't worry; I have a simpler definition to give you:
- A scalar is a number.
There. Wasn't that easy?
So multiplication of a scalar and a matrix simply means, multiplying a matrix by a number. Would you like to guess how we do that? It's pretty easy and straightforward; you just multiply each entry of the matrix by the scalar.Example One
If A = and k = 4, calculate kA. Solution
Mutliply each element of A times k: kA = Example Two
Calculate 6 Solution
Multiply each element of the matrix by 6: Example Three
Find x and y if x =
We can easily see that x = 6, since 1x = 6 and 6x = 36 (the first and third column products).
Looking at the second column, 5x = y, so 5(6) = y = 30.