Example 24 - Obtain inverse using elementary operations - Examples

Example 24 - Chapter 3 Class 12 Matrices - Part 2
Example 24 - Chapter 3 Class 12 Matrices - Part 3 Example 24 - Chapter 3 Class 12 Matrices - Part 4 Example 24 - Chapter 3 Class 12 Matrices - Part 5

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 2 Obtain the inverse of the following matrix using elementary operations A = [■8(0&1&2@1&2&3@3&1&1)] Given A = [■8(0&1&2@1&2&3@3&1&1)] We know that A = IA [■8(0&1&2@1&2&3@3&1&1)] = [■8(1&0&0@0&1&0@0&0&1)] A R1↔R2 [■8(𝟏&2&3@0&1&2@3&1&1)] = [■8(0&1&0@1&0&0@0&0&1)] A R3 → R3 – 3R1 [■8(1&2&3@0&1&2@𝟑−𝟑(𝟏)&1−3(2)&1−3(3))] = [■8(0&1&0@1&0&0@0−3(0)&0−3(1)&1−3(0))]A [■8(1&2&3@0&1&2@𝟎&−5&−8)] = [■8(0&1&0@1&0&0@0&−3&1)] R1 → R1 – 2R2 [■8(1−2(0)&𝟐−𝟐(𝟏)&3−2(2)@0&1&2@0&−5&−8)] = [■8(0−2(1)&1−2(0)&0−2(0)@1&0&0@0&−3&1)]A [■8(1&𝟎&−1@0&1&2@0&−5&−8)] = [■8(−2&1&0@1&0&0@0&−3&1)] A R3 → R3 + 5R2 [■8(1&0&−1@0&1&2@0+5(0)&−𝟓+𝟓(𝟏)&−8+5(2))] = [■8(−2&1&0@1&0&0@0+5(1)&−3+5(0)&1+5(0))] A [■8(1&0&−1@0&1&2@0&𝟎&2)] = [■8(−2&1&0@1&0&0@5&−3&1)] A R3 → 1/2 R3 [■8(1&0&−1@0&1&2@0/2&0/2&𝟐/𝟐)] = [■8(−2&1&0@1&0&0@5/2&(−3)/2&1/2)] A R1 → R1 + R3 [■8(1+0&0+0&−𝟏+𝟏@0&1&2@0&0&1)]=[■8(−2+5/2&1+((−3)/2)&0+1/2@1&0&0@5/2&(−3)/2&1/2)] A [■8(1&0&𝟎@0&1&2@0&0&1)] = [■8(1/2&(−1)/2&1/2@1&0&0@5/2&(−3)/2&1/2)] A R2 → R2 – 2R3 [■8(1&0&0@0−2(0)&1−2(0)&𝟐−𝟐(𝟏)@0&0&1)] = [■8(1/2&(−1)/2&1/2@1−2(5/2)&0−2((−3)/2)&0−2(1/2)@5/2&(−3)/2&1/2)]A [■8(1&0&0@0&1&𝟎@0&0&1)] = [■8(1/2&(−1)/2&1/2@−4&3&−1@5/2&(−3)/2&1/2)] A I= [■8(1/2&(−1)/2&1/2@−4&3&−1@5/2&(−3)/2&1/2)] A This is similar to I = A-1 A Hence, A-1 = [■8(𝟏/𝟐&(−𝟏)/𝟐&𝟏/𝟐@−𝟒&𝟑&−𝟏@𝟓/𝟐&(−𝟑)/𝟐&𝟏/𝟐)]

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.