![Ex 3.4, 12 - Find inverse of matrix [6 -3 -2 1] - Ex 3.4](https://cdn.teachoo.com/8c9f3880-8d60-4a42-88e8-9db4b48a7d7a/slide31.jpg)
Question 12 - Inverse of matrix using elementary transformation - Chapter 3 Class 12 Matrices
Last updated at Dec. 16, 2024 by Teachoo
Inverse of matrix using elementary transformation
Elementary operations on a matrix
You are here
You are here
Chapter 3 Class 12 Matrices
Concept wise
- Formation and order of matrix
- Types of matrices
- Equal matrices
- Addition/ subtraction of matrices
- Statement questions - Addition/Subtraction of matrices
- Multiplication of matrices
- Statement questions - Multiplication of matrices
- Solving Equation
- Finding unknown - Element
- Finding unknown - Matrice
- Transpose of a matrix
- Symmetric and skew symmetric matrices
- Proof using property of transpose
-
Inverse of matrix using elementary transformation
- Proof using mathematical induction
Transcript
Ex3.4, 12 Find the inverse of each of the matrices, if it exists.[■8(6&−3@−2&1)] Let A =[■8(6&−3@−2&1)] We know that A = IA [■8(6&−3@−2&1)]= [■8(1&0@0&1)] A R1 →1/6 R1 [■8(𝟔/𝟔&(−3)/6@−2&1)] = [■8(1/6&0/6@0&1)] A [■8(𝟏&(−1)/2@−2&1)] = [■8(1/6&0@0&1)] A R2 →R2 + 2R1 [■8(1&−1/2@−𝟐+𝟐(𝟏)&1+2((−1)/2) )] = [■8(1/6&0@0+2(1/6)&1+2(0))] A [■8(1&−1/2@𝟎&0)] = [■8(1/6&0@1/3&1)] A Since we have all zeros in the second row of the left hand side matrix of the above equation. Therefore, A-1 does not exist.
