Problem 3 based on Inverse of Matrix by Adjoint Method

TL;DR

This video demonstrates the process of finding the inverse of a matrix using the adjoint method.

Transcript

hello in this session we'll see third question on finding the inverse of metrics using a joint method so let's say we have a matrix of third order a with elements 4 6 9 6 0 -2 and 5 8 1. now we have to use a joint method so first of all let's try to find the formula required here will be 1 by determinant of a adjoin a so this determinant of this th... Read More

Key Insights

• 🗂️ The formula for finding the inverse of a matrix using the adjoint method is 1 divided by the determinant of the matrix multiplied by the adjoint matrix.
• 🤨 The determinant of a matrix can be calculated by expanding the matrix along a row or column, calculating the minors for each element, and performing the necessary calculations.
• ❓ The matrix of minors is obtained by calculating the minors for each element in the original matrix.
• 🧘 The matrix of cofactors is derived from the matrix of minors, with cofactors being negative for odd positions and the same as minors for even positions.
• 🥡 The adjoint matrix is obtained by taking the transpose of the matrix of cofactors.

Questions & Answers

Q: What is the formula for finding the inverse of a matrix using the adjoint method?

The formula is 1 divided by the determinant of the matrix multiplied by the adjoint matrix of the matrix.

Q: How do you calculate the determinant of a matrix?

To calculate the determinant, you expand the matrix along a row or column and calculate the minors of each element. Then, you multiply each element by its minor and alternate between addition and subtraction to obtain the determinant.

Q: What is the matrix of minors and how is it calculated?

The matrix of minors is obtained by calculating the minors of each element in the original matrix. To calculate a minor, you remove the row and column of the respective element and find the determinant of the remaining submatrix.

Q: How do you find the matrix of cofactors?

The matrix of cofactors is derived from the matrix of minors. The cofactors for odd positions are the negatives of the corresponding minors, while the cofactors for even positions remain the same as the minors.

Summary & Key Takeaways

• The video explains the formula required for finding the inverse of a matrix using the adjoint method.

• It demonstrates step-by-step calculations for finding the determinant and the matrix of minors.

• The video then shows how to find the matrix of cofactors by considering the odd and even positions.

• Finally, it explains how to find the adjoint matrix and obtain the inverse matrix using the determinant and adjoint matrix.