Ex 3.4, 2 - Find inverse of [2 1 1 1] - Chapter 3 Matrices - Inverse of matrix using elementary transformation

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise
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Ex3.4, 2 Find the inverse of each of the matrices, if it exists.[■8(2&1@1&1)] Let A = [■8(2&1@1&1)] We know that A = IA [■8(2&1@1&1)] = [■8(1&0@0&1)] A R1 →R1 – R2 [■8(𝟐−𝟏&1−1@1&1)] = [■8(1−0&0−1@0&1)] A [■8(𝟏&0@1&1)] = [■8(1&−1@0&1)] A R2 →R2 – R1 [■8(1&0@𝟏−𝟏&1−0)] = [■8(1&−1@0−1&1−(−1))] A [■8(1&0@𝟎&1)] = [■8(1&−1@−1&2)] A I = [■8(1&−1@−1&2)] A This is similar to I = A-1A Thus, A-1 = [■8(1&−1@−1" " &2" " )]

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