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Mike MᶜGarry

Matrices on the ACT

Lots of students have minor panic attacks when they are first faced with a matrix on the ACT Math Test, but never fear! Even if matrices look completely foreign to you, a quick read through this blog will calm your nerves. 🙂

Luckily, matrix questions are quite rare on the ACT (you might not see a single one throughout the 60 questions on the ACT Math Test!), and require only basic addition and subtraction skills (or *cough* a TI-83 calculator *cough*) to solve. If you can add 5 and 6, you’ll be fine!

The word matrix refers to a rectangular-looking box filled with numbers arranged in rows and columns Each number in the matrix is called an element.

Here’s How to Add Two Matrices


Notice that the size of the matrices is the same, and that each element in the first matrix is added to the corresponding element in the second matrix to get the corresponding element in the third matrix. -3 + -2 = -5.

With that understanding, we can solve for x by writing a simple equation: x + 9 = 11; x = 2.

Let’s look at a question involving subtracting matrices.

Guided ACT Matrix Practice Question


What is the sum of x and y?

To answer this, we will set up two equations to solve for x and y independently.

16 – 2 = x  and  3 – (-4) = y

14 = x and 7 = y

Their sum is 14 + 7 = 21.

Sometimes a variable will be introduced to stand for an entire matrix. Let’s look at an example:


Carefully subtract each corresponding element.

The Answer


Now try a practice question on your own!

Matrix Practice Question


What is the solution to the matrices?

(A) am_img6

(B) am_img7

(C) am_img8

(D) am_img9

(E) am_img10

The Answer & Explanation

The correct answer is (A).


To subtract matrices, subtract each corresponding element, as shown above. Remember that subtracting a negative number becomes addition.

With practice, you’ll see that the math involved in ACT matrix questions is rarely challenging – just keep the rows and columns lined up and you can’t help but get them right!


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About Mike MᶜGarry

Mike creates expert lessons and practice questions to guide GMAT students to success. He has a BS in Physics and an MA in Religion, both from Harvard, and over 20 years of teaching experience specializing in math, science, and standardized exams. Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets.

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