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 =

Solution
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.

1.

Explain the difference between a scalar and a matrix

2.

Find k if k =

3.

Find the value of x if x =

4.

If the product of a scalar and a matrix is a matrix with zero entries throughout, what can you conclude?

5.

If k = 3, h = 2, A = , B = , what is the first column, first column entry of kA + hB?