## How do you find the determinant by cofactor expansion?

# How do you find the determinant by cofactor expansion?

## How do you find the determinant by 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)).

### What is the determinant of a 4×4 matrix?

Determinant of a 4×4 matrix is a unique number that is also calculated using a particular formula. If a matrix order is in n x n, then it is a square matrix. So, here 4×4 is a square matrix that has four rows and four columns. If A is a square matrix then the determinant of the matrix A is represented as |A|.

#### How do you find determinant without cofactor expansion?

In order to find the determinant, we have to add the first and second rows. Now, we may factor (x + y + z) from the first row. After factor (x + y + z) first row and third row will be identical. Hence the answer is 0.

**When would you use cofactor expansion?**

Cofactor expansions are most useful when computing the determinant of a matrix that has a row or column with several zero entries. Indeed, if the ( i , j ) entry of A is zero, then there is no reason to compute the ( i , j ) cofactor.

**Can a determinant of a matrix be 0?**

When the determinant of a matrix is zero, the volume of the region with sides given by its columns or rows is zero, which means the matrix considered as a transformation takes the basis vectors into vectors that are linearly dependent and define 0 volume.

## How do you identify determinants?

Here are the steps to go through to find the determinant.

- Pick any row or column in the matrix. It does not matter which row or which column you use, the answer will be the same for any row.
- Multiply every element in that row or column by its cofactor and add. The result is the determinant.

### What does cofactor expansion do?

#### How do you expand a determinant?

Expanding to Find the Determinant

- Pick any row or column in the matrix. It does not matter which row or which column you use, the answer will be the same for any row.
- Multiply every element in that row or column by its cofactor and add. The result is the determinant.