Ex 3.4, 11 - Chapter 3 Class 12 Matrices (Term 1)

Transcript

Ex 3.4, 11 Find the inverse of each of the matrices, if it exists.[■8(2&−[email protected]&−2)] Let A =[■8(2&−[email protected]&−2)] We know that A = IA [■8(2&−[email protected]&−2)] = A [■8(1&[email protected]&1)] R1 → R1 – R2 [■8(𝟐−𝟏&−6−(−2)@1&−2)] = [■8(1−0&0−[email protected]&1)] A [■8(𝟏&−[email protected]&−2)] = [■8(1&−[email protected]&1)] A R2 → R2 – R1 [■8(1&−[email protected]𝟏−𝟏&−2−(−4))] = [■8(1&−[email protected]−1&1−(−1))] A [■8(1&−[email protected]𝟎&2)] = [■8(1&−[email protected]−1&2)] A R2 → 1/2 R2 [■8(1&−[email protected]𝟎/𝟐&2/2)] = [■8(1&−[email protected](−1)/2&2/2)] A [■8(1&−[email protected]𝟎&1)] = [■8(1&−[email protected](−1)/2&1)] A R1 → R1 + 4R2 [■8(1+4(0)&−𝟒+𝟒(𝟏)@0&1)] = [■8(1+4((−1)/2)&−1+4(1)@(−1)/2&1)] A [■8(1&𝟎@0&1)] = [■8(−1&[email protected](−1)/2&1)] A I = [■8(−1&[email protected](−1)/2&1)] A This is similar to I = A-1A Thus, A-1 = [■8(−𝟏&𝟑@(−𝟏)/𝟐&𝟏)]