# Determinant

## Determinant

Number associated with a table (or a matrix) of $$n^{2}$$ elements used to represent the sum of specific products of the elements in the table.

If there are $$n^{2}$$ elements, then there are n rows and n columns in the table.

Consider the matrix of order 2 : A = $$\begin{pmatrix}a_{1} & b_{1}\\a_{2} & b_{2}\end{pmatrix}$$
The determinant D of this matrix is : D = $$a_{1}b_{2} \space – \space a_{2}b_{1}$$

Cramer’s rule uses the notation of determinant to solve a system of linear equations.

### Example

Consider the matrix of order 2 : B = $$\begin{pmatrix}2 & 3\\-4 & 5\end{pmatrix}$$
The determinant D of this matrix is : D = $$a_{1}b_{2} \space – \space a_{2}b_{1}$$ = 10 – (–12) = 10 + 12 = 22