−2,−2,3
1,−3,0
−2,3,−2
Find the minor ⓐ a3 ⓑ b3 ⓒ c3
How do I set this up. I know how to use the 2x2 method but with 3x3 im confused.
To find the minor ⓐ a3 ⓑ b3 ⓒ c3, you need to create a submatrix by removing the third row and third column from the original matrix.
Given the matrix:
-2 -2 3
1 -3 0
-2 3 -2
To set up the 3x3 matrix, you can label the elements as follows:
a1 a2 ⓐ
a4 a5 ⓑ
a7 a8 ⓒ
Where the a1, a2, a4, a5, a7, and a8 are the elements of the original matrix.
By removing the third row and third column, the submatrix will be:
a1 a2 ⓐ
a4 a5 ⓑ
Now let's identify the corresponding elements from the original matrix:
a1 a2 ⓐ -> -2 -2 ⓐ
a4 a5 ⓑ -> 1 -3 ⓑ
So, the minor ⓐ a3 ⓑ b3 ⓒ c3 is:
-2 -2
1 -3
To find the determinant of this submatrix, you can use the 2x2 method. Find the product of the main diagonal (-2 * -3 = 6) and the product of the anti-diagonal (-2 * 1 = -2). Then subtract the product of the anti-diagonal from the product of the main diagonal (6 - (-2) = 8).
Therefore, the determinant of the minor ⓐ a3 ⓑ b3 ⓒ c3 is 8.