3x3 Matrices

Question 1

How to find cofactors

Answer 1

Cross out the number’s row and column and find the det. Change the sign accordingly.

Question 2

What are the cofactors?

Answer 2

+ - +.
- + -.
+ - +.

Question 3

Finding the inverse of a 3x3 matrix

Answer 3

1. Find cofactors.
2. Transpose cofactors.
3. Times original matrix and transposed matrix to find a multiple of the identiy matrix.
4. Times the transposed matrix by the reciprocal of the multiple of the identity matrix

Question 4

First step of finding the inverse of a 3x3 matrix

Answer 4

Find the cofactors

Question 5

Second step of finding the inverse of a 3x3 matrix

Answer 5

Transpose the cofactors (switch the rows and columns)

Question 6

Third step of finding the inverse of a 3x3 matrix

Answer 6

Times the original matrix and transposed matrix, it should equal a multiple of the identity matrix.

Question 7

Fourth step of finding the inverse of a 3x3 matrix

Answer 7

Times the transposed matrix by the reciprocal of the multiple of the identity matrix found.