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Ex 3.3
Ex 3.3, 2
Ex 3.3, 3
Ex 3.3, 4 Important
Ex 3.3, 5 (i)
Ex 3.3, 5 (ii)
Ex 3.3, 6 (i)
Ex 3.3, 6 (ii) Important
Ex 3.3, 7 (i)
Ex 3.3, 7 (ii) Important
Ex 3.3, 8 You are here
Ex 3.3, 9
Ex 3.3, 10 (i) Important
Ex 3.3, 10 (ii)
Ex 3.3, 10 (iii) Important
Ex 3.3, 10 (iv)
Ex 3.3, 11 (MCQ) Important
Ex 3.3, 12 (MCQ)
Last updated at May 29, 2023 by Teachoo
Ex 3.3, 8 For the matrix A = [■8(1&[email protected]&7)] , verify that (i) (A + A’) is a symmetric matrix A = [■8(1&[email protected]&7)] A’ = [■8(1&[email protected]&7)] A + A’ = [■8(1&[email protected]&7)] + [■8(1&[email protected]&7)] = [■8(2&[email protected]&14)] ∴ (A + A’)’ = [■8(2&[email protected]&14)] Since (A + A’)’ = A + A’ Hence, (A + A’) is a symmetric matrix. Ex 3.3, 8 For the matrix A = [■8(1&[email protected]&7)] , verify that (ii) (A – A’) is a skew symmetric matrix A = [■8(1&[email protected]&7)] A’ = [■8(1&[email protected]&7)] A – A’ = [■8(1&[email protected]&7)] − [■8(1&[email protected]&7)] = [■8(0&−[email protected]&0)] (A – A’)’ = [■8(0&1@−1&0)] = − [■8(0&−[email protected]&0)] = − (A – A’) Since, (A – A’)’ = – (A – A’) Hence, (A – A’) is a skew-symmetric matrix.