Question

How to find the determinant of a 3x3 matrix?

Answer 1

To find the determinant of a 3x3 matrix, you can use the cofactor expansion method. You multiply each element in each row by its corresponding cofactor, take the sum of these products for each row, and subtract and add these sums according to the specified formula.

Step-by-step explanation:

To find the determinant of a 3x3 matrix, you can use the cofactor expansion method. Here are the steps:

1. Multiply each element in the first row of the matrix by its corresponding cofactor.
2. Take the sum of these products.
3. Repeat steps 1 and 2 for the second and third rows.
4. Subtract the sum of the products from steps 1 and 2 for the second row from the sum of the products for the first row, and then add this difference to the sum of the products for the third row.

For example, if we have the matrix:

[ a b c ]

[ d e f ]

[ g h i ]

The determinant can be found using the following formula:

det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)

Answer 2

this is how

1. Write your 3 x 3 matrix. More ↓
2. Choose a single row or column. ↓
3. Cross out the row and column of your first element. ↓
4. Find the determinant of the 2 x 2 matrix. ↓
5. Multiply the answer by your chosen element. ↓
6. Determine the sign of your answer. ↓
7. Repeat this process for the second element in your reference row or column. ↓
8. Repeat with the third element. ↓
9. Add your three results together. ↓

Hope this helps!