Ex 3.4, 1 - Chapter 3 Class 12 Matrices (Term 1)

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Ex 3.4, 1 Find the inverse of each of the matrices, if it exists. [■8(1&−[email protected]&3)] Let A = [■8(1&−[email protected]&3)] We know that A = IA [■8(1&−[email protected]&3)] = [■8(1&[email protected]&1)] A R2 → R2 – 2R1 [■8(1&−[email protected]𝟐−𝟐(𝟏)&3−2(−1))] = [■8(1&[email protected]−2(1)&1−2(0))] A [■8(1&−[email protected]𝟎&5)] = [■8(1&[email protected]−2&1)] A R2 →1/5 R2 [■8(1&−[email protected]/5&𝟓/𝟓)] = [■8(1&[email protected](−2)/5&1/5)] A [■8(1&−[email protected]&𝟏)] = [■8(1&[email protected](−2)/5 " " &1/5 " " )] A R1 →R1 + R2 [■8(1+0&−𝟏+𝟏@0&1)] = [■8(1−2/5&0+1/[email protected](−2)/5 " " &1/5 " " )] A [■8(1&𝟎@0&1)] = [■8(3/5&1/[email protected](−2)/5 " " &1/5 " " )] A I = [■8(3/5&1/[email protected](−2)/5 " " &1/5 " " )] A This is similar to I = A-1A Thus, A-1 = [■8(𝟑/𝟓&𝟏/𝟓@(−𝟐)/𝟓 " " &𝟏/𝟓 " " )]