Question

Finding a determinant of a 3×3 matrix is done using:

A) Cofactor expansion
B) Inverse matrix
C) Transposition
D) Scalar multiplication

Answer 1

The correct method for finding the determinant of a 3x3 matrix is A) Cofactor expansion. To find the determinant, follow these steps: Multiply each element in each row of the matrix by its corresponding cofactor and add these products together. Take the sum of these products to find the determinant of the matrix.

Step-by-step explanation:

The correct method for finding the determinant of a 3x3 matrix is A) Cofactor expansion. To find the determinant, follow these steps:

1. Multiply each element in the first row of the matrix by its corresponding cofactor. Add these products together.
2. Multiply each element in the second row of the matrix by its corresponding cofactor. Add these products together.
3. Multiply each element in the third row of the matrix by its corresponding cofactor. Add these products together.
4. Take the sum of these three products to find the determinant of the matrix.

For example, if the 3x3 matrix is:
a b c
d e f
g h i
The determinant can be found using:

Determinant = (a * C11) + (b * C12) + (c * C13)