Examples

Chapter 3 Class 12 Matrices
Serial order wise

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### Transcript

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

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#### 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.