Question

How to find determinant of a 3x3 matrix?

A) Subtract the product of the diagonals.
B) Multiply the elements of the main diagonal.
C) Sum the products of diagonals going one way and subtract the other.
D) Sum all the elements in the matrix.

Answer 1

To find the determinant of a 3x3 matrix, sum the products of diagonals from the upper left to the lower right, then subtract the sum of products of diagonals going from the lower left to the upper right, which corresponds to option C.

Step-by-step explanation:

The correct method to find the determinant of a 3x3 matrix is option C: Sum the products of diagonals going one way and subtract the other. This process is also known as the rule of Sarrus. To calculate the determinant of a 3x3 matrix, you would perform the following steps:

1. Write down the elements of the first two columns of the matrix to the right of the third column.
2. Sum the products of the three diagonals going from the upper left to the lower right.
3. Subtract the sum of the products of the diagonals going from the lower left to the upper right.

This can be visualized as:

a b c a b

d e f d e

g h i g h

Sum(diagonals down) - Sum(diagonals up) = adi + beh + cfg - ceg - bdi - afh

The diagonal products starting from the leftmost column and moving down to the right are added, and the diagonal products that start from the rightmost column moving up to the left are subtracted from this sum.

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