How to find the eigenvectors of a matrix?

Finding eigenvectors of matrix

Let a square matrix of order $n\times n$ denoted by $A$ then eigen value is given by

$(A-\lambda I)$ where $I$ is an identity matrix of $n\times n$ same as order of matrix $A$ and $\lambda$ is any constant

Each eigen value is denoted ${\lambda }_1,{\lambda }_2,{\lambda }_3,.....$

Substitute the value in $AX={\lambda }_{1}x$

Calculate the value of eigenvector $x$ which is associated with eigenvalue ${\lambda }_1$.

Repeat the above step for ${\lambda }_2,{\lambda }_3,.....$

Hence in this way we can find the eigenvectors of a matrix.