## How do you expand a 3×3 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.

### What is the formula of determinant?

The determinant is: |A| = a (ei − fh) − b (di − fg) + c (dh − eg). The determinant of A equals ‘a times e x i minus f x h minus b times d x i minus f x g plus c times d x h minus e x g’. It may look complicated, but if you carefully observe the pattern its really easy!

#### What is the formula of cofactor?

One way of computing the determinant of an n×n n × n matrix A is to use the following formula called the cofactor formula. 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 a determinant on a graph?**

graph-theory determinants matrix-theory. In graph theory, we work with adjacency matrices which define the connections between the vertices. These matrices have various linear-algebraic properties.

**How to evaluate the determinant of a 3×3 matrix?**

In the last section of this lesson we will work through a set of three different 3×3 matrices and their determinants, we recommend you to compared the processes for both methods to understand them better. The process to evaluate the determinant of a matrix of greater dimensions than 3×3 follows the same logic than what we have seen so far.

## Is the determinant of a non square matrix?

The determinant of a non square matrix does not exist, only determinants of square matrices are defined mathematically. The determinant of a matrix can be denoted simply as det A, det (A) or |A|. This last notation comes from the notation we directly apply to the matrix we are obtaining the determinant of.

### Is there a shortcut to the determinant?

While the shortcut method is more of a clever trick we can use to simplify the calculation, still being careful to not forget numbers, the order in which they have to be multiplied and some rearrangements of the elements in the matrix.

#### How to find the determinant of a quadratic formula?

The formula to find the determinant for a quadratic formula is (b^2-4ac), which is all in a square root.