# ACT Math : How to find scalar interactions with a matrix

## Example Questions

### Example Question #8 : Find The Product Of A Matrix And A Scalar

Evaluate:

Explanation:

This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.

### Example Question #10 : Find The Product Of A Matrix And A Scalar

What is ?

Explanation:

You can begin by treating this equation just like it was:

That is, you can divide both sides by :

Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:

Then, simplify:

Therefore,

### Example Question #1 : Matrices

If , what is ?

Explanation:

Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of :

Now, this means that your equation looks like:

This simply means:

and

or

Therefore,

Simplify: