ACT Math : Matrices
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Example Questions
Example Question #9 : Other Matrices
Below is a matrix of the items in Jon's wardrobe:
How many combinations of blue pants and red shirts can Jon wear for the upcoming 4th of July party?
If Jon has three red shirts and two blue pants. The total number of combinations of one shirt and one pair of pants he can wear is going to be the number of shirts he can wear with the first pair of pants, 
Example Question #10 : Other Matrices
Read the following problem:
The barista at the Teahouse of the December Sun has a problem. He needs to mix twenty pounds of two different kinds of tea together to create a blend called Strawberry Peppermint Delight. The two varieties are Peppermint Nirvana, which costs $12 a pound, and Strawberry Fields, which costs $15 a pound; the new tea will cost $13 a pound, and it will sell for the same price as the two blended teas would separately. How much of each variety will go into the twenty pounds of Strawberry Peppermint Delight?
Which of the following augmented matrices represents the system of equations that could be set up to solve this problem?
If the barista mixes 
will be one of the equations in the system.
The augmented matrix of this system will comprise the coefficients of these equations, both of which are in standard form, so the matrix will be
Example Question #3 : Matrices
Simplify:
Matrix addition is very easy! All that you need to do is add each correlative member to each other. Think of it like this:
Now, just simplify:
There is your answer!
Example Question #4 : Matrices
Simplify:
Matrix addition is really easy—don't overthink it! All you need to do is combine the two matrices in a one-to-one manner for each index:
Then, just simplify all of those simple additions and subtractions:
Example Question #21 : Matrices
What is the value of
You cannot add these two matrices because their indices do not line up.
To add matrices you simply add the numbers in the same position as each other.
Plugging the given values into the above formula, we are able to solve the question.
Example Question #1 : How To Subtract Matrices
Given the following matrices, what is the product of 
When subtracting matrices, you want to subtract each corresponding cell.
Now solve for 
Example Question #1 : Find The Sum Or Difference Of Two Matrices
If 
You can treat matrices just like you treat other members of an equation. Therefore, you can subtract the matrix
from both sides of the equation. This gives you:
Now, matrix subtraction is simple. You merely subtract each element, matching the correlative spaces with each other:
Then, you simplify:
Therefore,
Example Question #1 : How To Subtract Matrices
When subtracting matrices, subtracting component-wise.
Example Question #21 : Matrices
If 
26
3
15
0
12
15
Match each term from the first matrix with the corresponding number from the second matrix and subtract.
Simplify.
Each of the numbers in the matrix solution now corresponds to the letters, a through f. Add a (upper left) and f (lower right).
Example Question #22 : Matrices
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter 
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