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Ex 3.4, 1 Find the inverse of each of the matrices, if it exists. [■8(1&−1@2&3)] Let A = [■8(1&−1@2&3)] We know that A = IA [■8(1&−1@2&3)] = [■8(1&0@0&1)] A R2 → R2 – 2R1 [■8(1&−1@𝟐−𝟐(𝟏)&3−2(−1))] = [■8(1&0@0−2(1)&1−2(0))] A [■8(1&−1@𝟎&5)] = [■8(1&0@−2&1)] A R2 →1/5 R2 [■8(1&−1@0/5&𝟓/𝟓)] = [■8(1&0@(−2)/5&1/5)] A [■8(1&−1@0&𝟏)] = [■8(1&0@(−2)/5 " " &1/5 " " )] A R1 →R1 + R2 [■8(1+0&−𝟏+𝟏@0&1)] = [■8(1−2/5&0+1/5@(−2)/5 " " &1/5 " " )] A [■8(1&𝟎@0&1)] = [■8(3/5&1/5@(−2)/5 " " &1/5 " " )] A I = [■8(3/5&1/5@(−2)/5 " " &1/5 " " )] A This is similar to I = A-1A Thus, A-1 = [■8(𝟑/𝟓&𝟏/𝟓@(−𝟐)/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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.