Question

How to find the determinant of a matrix 3x3.

A) Cofactor expansion
B) Matrix inversion
C) Gaussian elimination
D) Logarithmic expression

Answer 1

To find the determinant of a 3x3 matrix, you can use the cofactor expansion method. Here are the steps: Start by selecting any row or column of the matrix. For each element in the selected row or column, find its cofactor. Multiply each cofactor by its corresponding element in the matrix. Add or subtract these products to get the determinant.

Step-by-step explanation:

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

1. Start by selecting any row or column of the matrix.
2. For each element in the selected row or column, find its cofactor.
3. Multiply each cofactor by its corresponding element in the matrix.
4. Add or subtract these products to get the determinant.

For example, let's say we have the matrix:

| a b c |
| d e f |
| g h i |

If we select the first row, the cofactors would be:

(-1)^1 * det(e f h i) = e * det(h i) - f * det(g i) + h * det(g h) - i * det(g h)

Then, we can calculate the determinant using these cofactors.