If A =[a ij ] is a skew-symmetric matrix of order n, then

(a) a ij = 1/a ji  ∀ 𝑖,𝑗  

(b) a ij ≠ 0 ∀ 𝑖,𝑗

(c) a ij = 0, 𝑀ℎπ‘’π‘Ÿπ‘’ 𝑖 = 𝑗

(d) a ij ≠ 0 𝑀ℎπ‘’π‘Ÿπ‘’ 𝑖 = j

 

Slide1.JPG

Slide2.JPG

 

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 1 If A =[π‘Ž_𝑖𝑗 ] is a skew-symmetric matrix of order n, then (a) π‘Ž_𝑖𝑗 = 1/π‘Ž_𝑗𝑖 βˆ€ 𝑖,𝑗 (b) π‘Ž_𝑖𝑗 β‰  0 βˆ€ 𝑖,𝑗 (c) π‘Ž_𝑖𝑗 = 0, π‘€β„Žπ‘’π‘Ÿπ‘’ 𝑖 = 𝑗 (d) π‘Ž_𝑖𝑗 β‰  0 π‘€β„Žπ‘’π‘Ÿπ‘’ 𝑖 = j In a In a skew symmetric matrix A’ = βˆ’A For example If A = [β– 8(0&2&βˆ’3@βˆ’2&0&βˆ’9@3&9&0)] A’ = [β– 8(0&βˆ’2&3@2&0&9@βˆ’3&βˆ’9&0)] ∴ A’ = βˆ’A So, A is a skew symmetric matrix Now, We note that in every skew symmetric matrices Diagonal elements are zero i.e. a11 = 0, a22 = 0, a33 = 0 Thus, we can say that 𝒂_π’Šπ’‹ = 0, π‘€β„Žπ‘’π‘Ÿπ‘’ 𝑖 = 𝑗 So, the correct answer is (c)

Ask a doubt
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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.