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ACT Strategy for Solving a Matrix Using a Determinant

A determinant is a common operation performed on a square matrix. On the ACT Math test, the only determinant formula you need to be familiar with is for a 2 x 2 matrix. Here’s the formula for the determinant of

image0.png

Note that the determinant of a matrix is simply a number, not a matrix. To solve a problem with a determinant, you simply plug the numbers from the matrix into the formula and solve.

Example 1

What is the determinant of the matrix

image1.png

(A)    –22

(B)    –2

(C)    0

(D)    2

(E)    22

First, apply the determinant formula:

image2.png

Now evaluate to solve the problem:

= 28 – 30 = –2

Therefore, the correct answer is Choice (B).

Example 2

What is the value of k if the determinant of the matrix

image3.png

equals 16?

(F)    –2

(G)    –1

(H)    0

(J)    1

(K)    2

Start by applying the determinant formula and then evaluate:

image4.png

This value equals 16, so create your equation and solve:

image5.png

So the correct answer is Choice (F).

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