ACT Math : How to find scalar interactions with a matrix

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1064 : Algebra

Evaluate: 

Possible Answers:

Correct answer:

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 #1 : Matrices

What is ?

Possible Answers:

Correct answer:

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 #11 : Find The Product Of A Matrix And A Scalar

If , what is ?

Possible Answers:

Correct answer:

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, 

Example Question #1 : Find The Product Of A Matrix And A Scalar

Simplify:

Possible Answers:

Correct answer:

Explanation:

Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:

The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.

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