How to Find the Inverse of 3 × 3 Matrix?
Follow the steps given below in order to find the Inverse of 3 × 3 Matrix:
Step 1: Firstly, verify if the matrix can be inverted. To do this, calculate the determinant of the matrix. If the determinant is not zero, then proceed to the next step.
Step 2: Calculate the determinant of smaller 2 × 2 matrices within the larger matrix.
Step 3: Create the cofactor matrix.
Step 4: Obtain the Adjugate or Adjoint of the matrix by making the transpose of the cofactor matrix.
Step 5: Finally, divide each element in the adjugate matrix by the determinant of the original 3 by 3 matrix.
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Inverse of 3×3 Matrix
Inverse of a 3 × 3 matrix is a matrix which when multiplied by the original Matrix gives the identity matrix as the product. Inverse of a Matrix is a fundamental aspect of linear algebra. This process plays a crucial role in solving systems of linear equations and various mathematical applications. To calculate the inverse, it is required to calculate the adjoint matrix check the matrix’s invertibility by examining its determinant (which should not equal zero), and apply a formula to derive the Inverse Matrix.
This article covers the various concepts of the Inverse of 3 × 3 Matrix and how to Find the Inverse of 3 × 3 Matrix by calculating cofactors, adjoints, and determinants of 3 × 3 Matrix. Later in this article, you will also find solved examples for better understanding, and practice questions are also provided to check what we have learned from this.
Table of Content
- What is the Inverse of 3 × 3 Matrix?
- How to Find the Inverse of 3 × 3 Matrix?
- Elements Used to Find Inverse of 3 × 3 Matrix
- Inverse of 3 × 3 Matrix Formula
- Finding Inverse of 3 × 3 Matrix Using Row Operations
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