1. Determinants When taking the determinant of a matrix, we can “expand” by any row or any column

2. Step 1: Choose a row or column

3. Step 1: Choose a row or column Let’s choose the first row

4. *Always remember that signs alternate. This will make more sense later.

5. Step 2: Take the first number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers So we get 2 times the determinant of the matrix of non-circled numbers

6. Step 2: Take the first number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers So we get 2 times the determinant of the matrix of the numbers in the rectangle

7. Step 2: Take the first number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers 2*[(-5*6)-(8*0)] = 2*(-30-0) = -60

8. Step 2: Take the first number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers 2*[(-5*6)-(8*0)] = 2*(-30-0) = -60 THIS IS NOT THE FINAL ANSWER!

9. Step 3: Take the next number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers This is where the alternating signs come in

10. This is where the alternating signs come in Since the circled number is in the same position as a negative sign, we multiply it by negative 1 before multiplying it by the determinant of the 2x2 matrix in Step 4

11. Step 3: Take the next number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers -(-3)*[(5*-5)-(8*1)] = 3*(-25-8) = -99

12. Step 3: Take the next number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers -(-3)*[(5*-5)-(8*1)] = 3*(-25-8) = -99 THIS IS NOT THE FINAL ANSWER!

13. Step 4: Take the last number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers 11*[(5*0)-(6*1) = 11*(0-6) = -66

14. Step 4: Take the last number in our row and multiply it by the determinant of the matrix left after eliminating all adjacent numbers 11*[(5*0)-(6*1) = 11*(0-6) = -66 THIS IS NOT THE FINAL ANSWER!

15. We now have the three parts of our answer. To find the actual answer, we take the sum of our three parts -60 -99 -66 = -225 So the determinant of our matrix is -225