Ex 3.4, 9 - Class 12

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Ex3.4, 9 Find the inverse of each of the matrices, if it exist [■8(3&10@2&7)] Let A = [■8(3&10@2&7)] We know that A = IA [■8(3&10@2&7)]= [■8(1&0@0&1)] A R1 → R1 – R2 [■8(𝟑−𝟐&10−7@2&7)]= [■8(1−0&0−1@0&1)] A [■8(𝟏&3@2&7)]= [■8(1&−1@0&1)] A R2 → R2 – 2R1 [■8(1&3@𝟐−𝟐(𝟏)&7−2(3))]= [■8(1&−1@0−2(1)&1−2(−1))] A [■8(1&3@𝟐−𝟐&7−6)]= [■8(1&−1@0−2&1+2)] A [■8(1&3@𝟎&1)]= [■8(1&−1@−2&3)] A R1 → R1 – 3R2 [■8(1−3(0)&𝟑−𝟑(𝟏)@0&1)]= [■8(1−3(−2)&−1−3(3)@−2&3)] A [■8(1−0&𝟑−𝟑@0&1)]= [■8(1+6&−1−9@−2&3)] A [■8(1&𝟎@0&1)]= [■8(7&−10@−2&3)] A I = [■8(7&−10@−2&3)] A This is similar to I = A-1 A Thus A-1 =[■8(7&−10@−2&3)]