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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&2@2&−1)] Given A = [■8(1&2@2&−1)] We know that A = IA [■8(1&2@2&−1)] = [■8(1&0@0&1)] A R2 → R2 – 2R1 [■8(1&2@𝟐−𝟐(𝟏)&−1−2(2))] = [■8(1&0@0−2(1)&1−2(0))] A [■8(1&2@𝟐−𝟐&−1−4)] = [■8(1&0@0−2&1−0)] A [■8(1&2@𝟎&−5)] = [■8(1&0@−2&1)] A R2 → (−1)/5 R2 [■8(1&2@0((−1)/5)&−𝟓((−𝟏)/𝟓) )] = [■8(1&0@−2((−1)/5)&1((−1)/5) )]A [■8(1&2@0&𝟏)] = [■8(1&0@2/5&(−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&2/5@2/5&(−1)/5)] A [■8(1&𝟎@0&1)] = [■8(1/5&2/5@2/5&(−1)/5)] A I = [■8(1/5&2/5@2/5&(−1)/5)] A This is similar to I = A-1 A Hence A-1 = [■8(1/5&2/5@2/5&(−1)/5)]

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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.