Question

How do you go about finding the determinant of a 3x3 matrix?

Answer 1

To find the determinant of a 3x3 matrix, use the Rule of Sarrus by summing the products of diagonals from top left to bottom right, then subtracting the sum of the products of diagonals from bottom left to top right.

Step-by-step explanation:

Finding the Determinant of a 3x3 Matrix

To find the determinant of a 3x3 matrix, you can follow these steps which involve a method called the Rule of Sarrus:

1. Write down the matrix and copy the first two columns of the matrix to the right of the third column.
2. Draw diagonals from top left to bottom right and calculate the products of the numbers in these diagonals. Sum up these products.
3. Now, draw diagonals from bottom left to top right, calculate the products of the numbers in these diagonals and sum them up.
4. Subtract the sum of the second set from the first set, and this result is the determinant of the matrix.

An example is when you calculate the determinant of matrix A:

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

The determinant, denoted as det(A), would be computed as:

(aei + bfg + cdh) - (gec + hfa + idb)

There are other methods like Laplace's expansion, also known as cofactor expansion, which is more systematic and works for any size matrix.

Remember, the determinant provides important information about the matrix, such as whether the matrix is invertible or not.