On the previous page, we learned that, unlike matrices, which are really just arrays of numbers, determinants can be evaluated, which simply means that they have a numerical value which can be calculated. To learn how to calculate the value of a determinant, we will begin with a 2 x 2 determinant.

= ad - bc.

That's it! Multiply the top left entry by the bottom right entry, and then subtract from it the product of the other two elements. Let's try it with a determinant that has numerical entries:

Problem One
Evaluate

Solution
1(5) - 3(2) = 5 - 6 = -1.

We can make this more interesting by using variables in our determiants:

Problem Two
Solve for x if = 16

Solution
3x - 2 = 16
3x = 18
x = 6

Problem Three
Solve for x if = 5x

Solution
x² - 6 = 5x
x² - 5x - 6 = 0
(x - 6)(x + 1) = 0
x = 6 or x = -1

Problem Four
Solve for x if x = 2x - 24

Solution
First we evaluate the determinant: 2(3) - 2(1) = 6 - 2 = 4

So 4x = 2x - 24
2x = -24
x = -12

1.

Find the value of

2.

Find the value of

3.

Find the value of

4.

Find x if = 7

5.

Find x if =8x - 30

6.

Find x if =

7.

Find x if = -6