Ex 3.4, 1

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Ex3.4, 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 " " )]