JEE Exam  >  JEE Videos  >  Mathematics (Maths) Class 12  >  Solving a system of Linear Equations Using Inverse of a Matrix Part 1

Solving a system of Linear Equations Using Inverse of a Matrix Part 1 Video Lecture | Mathematics (Maths) Class 12 - JEE

204 videos|288 docs|139 tests

Timeline

00:03 Solving equations using Matrices & Determinants
00:25 Write equations in Matrix form - Matrix of Coefficients
01:17 Multiplication of Matrices
02:37 Using Matrix form to solve the equation

FAQs on Solving a system of Linear Equations Using Inverse of a Matrix Part 1 Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the inverse of a matrix?
Ans. The inverse of a matrix is a matrix that, when multiplied with the original matrix, gives the identity matrix. It is denoted by A^-1, where A is the original matrix.
2. How can the inverse of a matrix be used to solve a system of linear equations?
Ans. To solve a system of linear equations using the inverse of a matrix, we can represent the system as a matrix equation AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants. By multiplying both sides of the equation by A^-1, we can isolate X and solve for the variables.
3. Can every matrix have an inverse?
Ans. No, not every matrix has an inverse. Only square matrices that have a non-zero determinant have an inverse. If the determinant of a matrix is zero, it is called a singular matrix and does not have an inverse.
4. What is the determinant of a matrix?
Ans. The determinant of a square matrix is a scalar value that can be computed from its elements. It provides information about the matrix, such as whether it has an inverse and how it scales the space it operates on. The determinant is denoted by det(A) or |A|.
5. Are there any limitations or challenges in using the inverse of a matrix to solve systems of linear equations?
Ans. Yes, there are some limitations and challenges in using the inverse of a matrix. One limitation is that it is computationally expensive to calculate the inverse of a large matrix. Additionally, if the matrix is nearly singular or ill-conditioned, numerical errors may arise during the calculation of the inverse, leading to inaccurate solutions.
204 videos|288 docs|139 tests

Up next

Explore Courses for JEE exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Exam

,

practice quizzes

,

past year papers

,

video lectures

,

study material

,

Solving a system of Linear Equations Using Inverse of a Matrix Part 1 Video Lecture | Mathematics (Maths) Class 12 - JEE

,

Sample Paper

,

Solving a system of Linear Equations Using Inverse of a Matrix Part 1 Video Lecture | Mathematics (Maths) Class 12 - JEE

,

pdf

,

Previous Year Questions with Solutions

,

Semester Notes

,

Free

,

Viva Questions

,

Objective type Questions

,

Summary

,

MCQs

,

ppt

,

shortcuts and tricks

,

Important questions

,

Extra Questions

,

Solving a system of Linear Equations Using Inverse of a Matrix Part 1 Video Lecture | Mathematics (Maths) Class 12 - JEE

,

mock tests for examination

;