Check sibling questions

Ex 3.3, 8 - For A = [1 5 6 7], verify (i) (A + A') is symmetric - Symmetric and skew symmetric matrices

Ex 3.3, 8 - Chapter 3 Class 12 Matrices - Part 2


Transcript

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&[email protected]−1&0)] = − [■8(0&−[email protected]&0)] = − (A – A’) Since, (A – A’)’ = – (A – A’) Hence, (A – A’) is a skew-symmetric matrix.

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.