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Kristin Fracchia

TuesdACT Video: How to Tackle Matrices on the ACT


Today’s TuesdACT video is a lightning fast refresher on matrices!

Matrices on the ACT are something that aren’t as scary as they might initially seem. In advanced math and statistics, matrices serve some important purposes, but if you’re wondering what the heck they could possibly be useful for right now–you aren’t alone. That’s ok because, first of all, you aren’t going to encounter many matrices on the ACT. Maybe you’ll see one, maaaaaybe two, and often zero.

BUT if you want a top score on the ACT, it’s useful to know how they work.

When it comes to matrices on the test, you really just need to know the basics:


First of all, matrices are referred to by their dimensions.

Matrices can come in all sorts of sizes. We write the size of a matrix first with its number of rows and then its number of columns.

This, for example, is a 3 x 2 matrix. 3 rows and 2 columns:



Scalar Multiplication

You might see a question on the ACT that asks you do what is called scalar multiplication. This means that we are multiplying a matrix by an ordinary number. Every entry inside the matrix just gets multiplied by that number.



Matrix Addition

You might also see a question on the ACT on adding or subtracting matrices. Important note: you can only add or subtract two matrices of exactly the same dimensions.  We add or subtract matrices by adding or subtracting the corresponding numbers (the numbers that are in the same “spot” on each matrix).



Multiplying Matrices

Alright, I saved the trickiest for last. You can only multiply matrices if the number of columns in first matrix equals the number of rows in the second matrix. When we multiply matrices, the product matrix will have the same number of rows as first matrix and the same number of columns as the second. For example, the product of a 2 x 3 matrix and a 3 x 2 matrix would be a 3 x 3 matrix.


In order to find the entry in the first column, first row of the product matrix, we are going to multiply each number in the first row of the first matrix by its corresponding number in the first column of the second matrix and add the products together.


For the entry in the second row, second column, we will do the same thing with the second row of the first matrix and the second column of the second matrix:


In order to completely fill out this matrix, we would have to do 9 calculations, but don’t fret, the ACT is more likely to give you smaller matrices or matrices with more zeros or ask you to find just one entry in a matrix.

There you are. That wasn’t so bad 🙂 . Check out the video above for more on mastering matrices on the ACT!


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About Kristin Fracchia

Kristin makes sure Magoosh's sites are full of awesome, free resources that can be found by students prepping for standardized tests. With a PhD from UC Irvine and degrees in Education and English, she’s been working in education since 2004 and has helped students prepare for standardized tests, as well as college and graduate school admissions, since 2007. She enjoys the agony and bliss of train running, backpacking, hot yoga, and esoteric knowledge.

2 Responses to “TuesdACT Video: How to Tackle Matrices on the ACT”

  1. Camden S. says:

    Wait… Wouldn’t the matrix at the beginning of the video be a 2 x 3 matrix? It has 2 horizontal rows and 3 vertical columns, and they are named row x column. In the written portion as well, shouldn’t the first matrix be a 3 x 2? Correct me if I’m wrong… the whole row and column business confused me in my college algebra class and still does haha.

    • Kristin Fracchia Kristin Fracchia says:

      Thanks, Camden. Apparently, I had an embarrassing brain cramp and momentarily forgot the definition of rows and columns! Sheesh :P. You are right, of course. That’s my silly error. I fixed the blog post, and we will correct the video!

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