3x3 Determinants

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3x3 MatricesFinding Determinants :

3x3 MatricesFinding Determinants There are two methods that are commonly used to find the determinant of a 3x3 Matrix: Expansion Method Diagonals Method Sometimes the expansion method will be easier to use than the diagonal method and sometimes it will be the other way around. It depends on the numbers in the matrix itself.

Expansion Method :

Expansion Method The is called expansion along row 1. Notice the sign pattern For a, b and c: + - +. It will be this pattern for row 1 and row 3 And also for column 1 and column 3.

Expansion using Column 2 :

Expansion using Column 2 Notice that the sign pattern has changed to - + -. It will be this Way for row 2 and column 2.

Example: Find the determinant of the matrix by expanding along row 3. :

Example: Find the determinant of the matrix by expanding along row 3.

Example: Find the determinant of the matrix by expanding along column 2. :

Example: Find the determinant of the matrix by expanding along column 2.

Diagonals Method :

Diagonals Method When using the diagonals method, copy the 2 columns down as usual, then add columns 1 and 2 to the end so you end up with 3 rows and 5 columns. After doing this, there will be three diagonals Going down from left to right and three diagonals going down from Right to left. Each diagonal must contain 3 numbers.

Example: Find the determinant using the diagonals method. :

Example: Find the determinant using the diagonals method.