The inverse of 3 x 3 matrices with matrix row operations

The inverse of 3 x 3 matrices with matrix row operations

In this section, you will learn how to find the inverse of a 3 x 3 matrix. This method requires the use of matrix row operation. The idea is to draw a vertical line in the middle, write the matrix on the left side of the line, and write the 3 x 3 identity matrix on the right side of the line. Then the goal is to do a bunch of matrix row operation so that the identity matrix appears on the left side of the line. Whatever appears on the right side will be the inverse. Note that this method works for 2 x 2 matrices as well, except the right side of the line is a 2 x 2 identity matrix.
Basic concepts: The three types of matrix row operations, Solving a linear system with matrices using Gaussian elimination, Identity matrix,
Related concepts: The inverse of 3 x 3 matrix with determinants and adjugate,

Lessons

This is a lot different from finding inverses of 2 x 2 matrices from the previous section, so start with a fresh mind when finding the inverse of 3 x 3 matrices. This method also works for any square matrix!
  • Introduction
    The Inverse of 3 x 3 Matrix using matrix row operations
  • 1.
    Finding the Inverse
    You are given that The inverse of 3 x 3 matrices with matrix row operations. Find the inverse of this matrix.
  • 2.
    You are given that The inverse of 3 x 3 matrices with matrix row operations. Find the inverse of this matrix.
  • 3.
    You are given that The inverse of 3 x 3 matrices with matrix row operations. Find the inverse of this matrix.
  • 4.
    You are given that The inverse of 3 x 3 matrices with matrix row operations. Find the inverse of this matrix.
  • 5.
    You are given that The inverse of 3 x 3 matrices with matrix row operations. Find the inverse of this matrix.
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22.
Determinants and Inverses of Matrices
22.1
The determinant of a 2 x 2 matrix
22.2
The determinant of a 3 x 3 matrix (General & Shortcut Method)
22.3
The inverse of a 2 x 2 matrix
22.4
The inverse of 3 x 3 matrices with matrix row operations
22.5
The inverse of 3 x 3 matrix with determinants and adjugate
22.6
2 x 2 invertible matrix
22.7
Solving linear systems using Cramer's Rule
22.8
Solving linear systems using 2 x 2 inverse matrices
Grade 12 Math