CBSE Class 12 Sample Paper for 2023 Boards

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Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Question 1 - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 13, 2024 by

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

 

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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)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo