Check sibling questions

The value of |A|, if A=[0 2x-1 √x 1-2x 0 2√x -√x -2√x 0)], where x∈R^+, is

(a) (2x+1)^2         (b) 0             (c) (2x+1)^3            (d) (2x-1)^2




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Given 𝐴=[β– (0&2π‘₯βˆ’1&√π‘₯@1βˆ’2π‘₯&0&2√π‘₯@βˆ’βˆšπ‘₯&βˆ’2√π‘₯&0)] Since diagonal elements are 0, this might be a skew symmetric matrix Let’s check Finding 𝑨^𝑻 𝐴^𝑇=[β– (0&1βˆ’2π‘₯&βˆ’βˆšπ‘₯@2π‘₯βˆ’1&0&βˆ’2√π‘₯@√π‘₯&2√π‘₯&0)] 𝐴^𝑇=βˆ’[β– (0&2π‘₯βˆ’1&√π‘₯@1βˆ’2π‘₯&0&2√π‘₯@βˆ’βˆšπ‘₯&βˆ’2√π‘₯&0)] 𝑨^𝑻= βˆ’ A Since 𝐴^𝑇= βˆ’A ∴ A is a skew symmetric matrix of order 3 We know that , Determinant of every skew symmetric matrix of odd order is 0. ∴ |A| = 0 So, the correct answer is (b)

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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.