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If [(0,2b,c),(a,b,-c),(a,-b,c)] is orth...

If `[(0,2b,c),(a,b,-c),(a,-b,c)]` is orthogonal matrix, then the value of `|abc|` is equal to (where `|*|` represents modulus function)

A

`a=pm1/sqrt(2),b=pm1/sqrt(6),c=pm1/sqrt(3)`

B

`a=pm1/sqrt(2),b=pm1/sqrt(3),c=pm1/sqrt(6)`

C

`a=pm1/sqrt(6),b=pm1/sqrt(2),c=pm1/sqrt(3)`

D

`a=pm1/sqrt(3),b=pm1/sqrt(2),c=pm1/sqrt(6)`

Text Solution

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The correct Answer is:
A
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DISHA PUBLICATION-MATRICES-Exercise 2: Concept Applicator
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  7. IfA^(k)= 0 (Ais nilpotent with index k), (I-A)^(p)=I+A+A^(2)+. . .+A^(...

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  8. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

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  9. If A=[(1,-1),(2,-1)] and B=[(1,a),(4,b)] and (A+B)^(2)=A^(2)+B^(2). ...

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  11. If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n d...

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  14. If {:A=[(alpha,0),(1,1)]andB=[(1,0),(5,1)]:}, then te value of alpha f...

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  15. [[i,0,0],[0,i,0],[0,0,i]] then A^(4n+1) =.... n in N

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  16. The matrix A=[0-5 8 5 0 12-8-12 0] is a (a) diagonal matrix (b) symmet...

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  17. If A=[(alpha,0),(1,1)] and B=[(9,a),(b,c)] and A^(2)=B, then the value...

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  18. Find the value of k so that A^2=8A+kI where A=[(1,0),(-1,7)].

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  19. A square matrix P satisfies P^(2)=I-P where I is identity matrix. If P...

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  20. If A(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)], then

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