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Example 23 - By using elementary operations, find inverse

Example 23 - Chapter 3 Class 12 Matrices - Part 2
Example 23 - Chapter 3 Class 12 Matrices - Part 3

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Transcript

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

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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.