Ex 3.3, 9 - Chapter 3 Class 12 Matrices

Transcript

Ex 3.3, 9 Find 1/2 (A + A’)and 1/2 (A – A’) , when A = [■8(0&a&b@−a&0&c@−b&−c&0)] A = [■8(0&a&b@−a&0&c@−b&−c&0)] A‘ = [■8(0&−a&−b@a&0&−c@b&c&0)] 1/2 (A + A’) = 1/2 ([■8(0&a&b@−a&0&c@−b&−c&0)]"+" [■8(0&−a&−b@a&0&−c@b&c&0)]) = 1/2 [■8(0&0&0@0&0&0@0&0&0)] = [■8(0&0&0@0&0&0@0&0&0)] 1/2 (A − A’) = 1/2 ([■8(0&a&b@−a&0&−c@−b&−c&0)]−[■8(0&−a&−b@a&0&−c@b&c&0)]) = 1/2 [■8(0&2a&2b@−2a&0&2c@−2b&−2c&0)] = [■8(1/2×0&1/2×2a&1/2×2b@1/2×−2a&1/2×0&1/2×2c@1/2×−2b&1/2×−2c&1/2×0)] = [■8(0&a&b@−a&0&c@−b&−c&0)]