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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 June 8, 2023 by Teachoo
Ex 3.3, 8 For the matrix A = [■8(1&5@6&7)] , verify that (i) (A + A’) is a symmetric matrix A = [■8(1&5@6&7)] A’ = [■8(1&6@5&7)] A + A’ = [■8(1&5@6&7)] + [■8(1&6@5&7)] = [■8(𝟐&𝟏𝟏@𝟏𝟏&𝟏𝟒)] ∴ (A + A’)’ = [■8(𝟐&𝟏𝟏@𝟏𝟏&𝟏𝟒)] Since (A + A’)’ = A + A’ Hence, (A + A’) is a symmetric matrix. Ex 3.3, 8 For the matrix A = [■8(1&5@6&7)] , verify that (ii) (A – A’) is a skew symmetric matrix A = [■8(1&5@6&7)] A’ = [■8(1&6@5&7)] A – A’ = [■8(1&5@6&7)] − [■8(1&6@5&7)] = [■8(𝟎&−𝟏@𝟏&𝟎)] (A – A’)’ = [■8(0&1@−1&0)] = − [■8(0&−1@1&0)] = − (A – A’) Since, (A – A’)’ = – (A – A’) Hence, (A – A’) is a skew-symmetric matrix.