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How To Find Inverse Of A Matrix

In the previous article, you learned about Inverse of Matrix and why it is important. We will explore how to find inverse of a matrix in this article. There are two primary method of finding inverse of any square invertible matrix – Classical adjoint method and Gauss -Jordan elimination method.

Methods To Find Inverse Of Matrix

The primary method of finding of inverse of matrix are

  1. Classical adjoint method
  2. Gauss-Jordan elimination method

Throughout this article, we will discuss about these two methods in detail.

Classical Adjoint Method

If A is an invertible matrix then we can find the inverse of matrix A with the adjoint of matrix A.

But,before we begin you must understand a few terminologies.

Determinant – It is a special number obtained from a Square Matrix, non-square matrix do not have determinants. If A is a square matrix then there is a number of ways to denote its determinant.

A = \begin{bmatrix}a & b\\c & d\end{bmatrix}det(A) or \begin{vmatrix}A\end{vmatrix} or \begin{vmatrix}a & b\\c & d\end{vmatrix}det(A)= ad - bc

Minor of a matrix – The minor of a square matrix is determinant obtained by deleting a row and a column from the determinant of a larger square matrix. It is denoted by M_{ij} for element a_{ij} where i is the ithrow and j is the jth column.

The determinant of 2 x 2 matrix

det(A) =\begin{vmatrix}a & b\\c & d\end{vmatrix}M_{11} = \begin{vmatrix}a & b\\c & d\end{vmatrix} = \begin{vmatrix}d\end{vmatrix}M_{12} = \begin{vmatrix}a & b\\c & d\end{vmatrix} = \begin{vmatrix}c\end{vmatrix}M_{21} = \begin{vmatrix}a & b\\c & d\end{vmatrix} = \begin{vmatrix}b\end{vmatrix}M_{11} = \begin{vmatrix}a & b\\c & d\end{vmatrix} = \begin{vmatrix}a\end{vmatrix}

The post How To Find Inverse Of A Matrix appeared first on Notesformsc.

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How To Find Inverse Of A Matrix


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