Question

Suppose A is an n x n matrix. How do you find the determinant of A ?

Answer 1

To find the determinant of an n x n matrix, you can use various methods such as cofactor expansion or row reduction. One common method is using cofactor expansion along the first row or column. Here's a step-by-step process: 1) Choose the first row or column of the matrix. 2) Multiply each element in the chosen row or column by its cofactor. 3) Alternate the signs of the products. 4) Sum up the products to get the determinant of the matrix.

Step-by-step explanation:

To find the determinant of an n x n matrix, you can use various methods such as cofactor expansion or row reduction. One common method is using cofactor expansion along the first row or column.

Here's a step-by-step process:

1. Choose the first row or column of the matrix.
2. Multiply each element in the chosen row or column by its cofactor (the determinant of the submatrix formed by deleting the row and column of that element).
3. Alternate the signs of the products, starting with a positive sign for the first element.
4. Sum up the products to get the determinant of the matrix.

For example, let's say we have a 3 x 3 matrix A:

A = [[a, b, c], [d, e, f], [g, h, i]]

The determinant of A can be calculated as:

det(A) = a(det([[e, f], [h, i]])) - b(det([[d, f], [g, i]])) + c(det([[d, e], [g, h]]))