Table of Contents

## How do you find the determinant of a 3×3 matrix using cofactor expansion?

How to compute the cofactor expansion 3×3?

- Choose a row/column of your matrix. Go for the one containing the most zeros.
- For each coefficient in your row/column, compute the respective 2×2 cofactor.
- Multiply the coefficient by its cofactor.
- Add the three numbers obtained in steps 2 & 3.
- This is your determinant!

**How do you find the determinant of cofactor expansion?**

One way of computing the determinant of an n×n matrix A is to use the following formula called the cofactor formula. Pick any i∈{1,…,n}. Then det(A)=(−1)i+1Ai,1det(A(i∣1))+(−1)i+2Ai,2det(A(i∣2))+⋯+(−1)i+nAi,ndet(A(i∣n)).

**Can we use column operations to find determinant?**

(Uses the formal definition of the determinant). This means that you can also use elementary column operations to evaluate determinants as well, since a column operation on A has the same effect as the corresponding row operation on AT.

### How do you find the determinant of a 4×4 matrix?

Linear Algebra: Find the determinant of the 4 x 4 matrix A = [1 2 1 0 \\ 2 1 1 1 \\ -1 2 1 -1 \\ 1 1 1 2] using a cofactor expansion down column 2. This is largely an exercise in bookkeeping.

**What is the determinant of a 3×3 matrix?**

For example, let A be the following 3×3 square matrix: The minor of 1 is the determinant of the matrix that we obtain by eliminating the row and the column where the 1 is.

**How to find the minor and cofactor of a matrix?**

For example, let A be the following 3×3 square matrix: The minor of 1 is the determinant of the matrix that we obtain by eliminating the row and the column where the 1 is. That is, removing the first row and the second column: On the other hand, the formula to find a cofactor of a matrix is as follows: Where M ij is the i, j minor of the matrix.

## What is the difference between the minor of 1 and cofactor?

The minor of 1 is the determinant of the matrix that we obtain by eliminating the row and the column where the 1 is. That is, removing the first row and the second column: On the other hand, the formula to find a cofactor of a matrix is as follows: Where M ij is the i, j minor of the matrix.