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 $2 \times 2$ 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: $\begin{bmatrix} -2 & 7 \\ 4 & 5 \end{bmatrix}$ 

Solution:

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

$-2\times 5-7\times 4=-38$

 


Practise This Question

The dissociation energy of H2 is 430.53 kJ mol1. If hydrogen is dissociated by illumination with radiation of wavelength 253.7 nm, the fraction of the radiant energy which will be converted into kinetic energy is given by