 # Matrix Formula

Matrix is a way of arrangement of numbers, sometimes expressions and symbols, in rows and columns. Matrix formulas are used to solve linear equations and calculus, optics, quantum mechanics and other mathematical functions. If the two matrix are of the same size as their rows and columns, then they can be added, subtracted and multiplied element by element.

If you see a

$$\begin{array}{l}2 \times 2\end{array}$$
matrix, then that means the matrix has 2 rows and 2 columns.

$\large A=\begin{bmatrix} a11 & a12\\ a21 & a22 \end{bmatrix}$

The adjoint of a 2×2 matrix is given as,

$\large adj(A)=\begin{bmatrix} a22 & -a12\\ -a21 & a11 \end{bmatrix}$

The inverse of a 2×2 matrix is given as,

$\large A^{-1}=\frac{1}{|A|}\times adj(A)$

### Solved Examples

Question: Find out the determinant of the matrix:

$$\begin{array}{l}\begin{bmatrix} -2 & 7 \\ 4 & 5 \end{bmatrix}\end{array}$$

Solution:

The determinant is given by the formula: |A| = ad – bc

$$\begin{array}{l}-2\times 5-7\times 4=-38\end{array}$$

 More topics in Matrix Formula Discriminant Formula Determinant Formula Inverse Matrix Formula Cofactor Formula Covariance Matrix Formula