Question 1 - Examples - Chapter 3 Class 12 Matrices
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo