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
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
(A) –22
(B) –2
(C) 0
(D) 2
(E) 22
First, apply the determinant formula:
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
equals 16?
(F) –2
(G) –1
(H) 0
(J) 1
(K) 2
Start by applying the determinant formula and then evaluate:
This value equals 16, so create your equation and solve:
So the correct answer is Choice (F).