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 Oct. 11, 2022 by Teachoo

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, 𝑤ℎ𝑒𝑟𝑒 𝑖 = 𝑗

(d) a
_{
ij
}
≠ 0 𝑤ℎ𝑒𝑟𝑒 𝑖 = j

Transcript

Question 1 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, 𝑤ℎ𝑒𝑟𝑒 𝑖 = 𝑗 (d) 𝑎_𝑖𝑗 ≠ 0 𝑤ℎ𝑒𝑟𝑒 𝑖 = j In a In a skew symmetric matrix
A’ = −A
For example
If A = [■8(0&2&−[email protected]−2&0&−[email protected]&9&0)]
A’ = [■8(0&−2&[email protected]&0&[email protected]−3&−9&0)]
∴ A’ = −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_𝒊𝒋 = 0, 𝑤ℎ𝑒𝑟𝑒 𝑖 = 𝑗
So, the correct answer is (c)

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.

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