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[(x,y,z)][(a,h,g),(h,b,f),(g,f,c)][(x),(...

`[(x,y,z)][(a,h,g),(h,b,f),(g,f,c)][(x),(y),(z)]=`

A

`[ax^(2)+by^(2)+cz^(2)+2hxy+2gxz+2fyz]`

B

`[ax^(2)+by^(2)+cz^(2)+hxy+gxz+fyz]`

C

`[2ax^(2)+2by^(2)+2cz^(2)+hxy+gxz+fyz]`

D

`[2ax^(2)+2by^(2)+2cz^(2)+2hxy+2gxz+2fyz]`

Text Solution

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A
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AAKASH SERIES-MATRICES -ALGEBRA OF MATRICES - EXERCISE - II
  1. If AB=A,BA=B then A^(2)+B^(2)=

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  2. If A=[(3,0,0),(0,3,0),(0,0,3)] then A^(5)=

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  3. [(x,y,z)][(a,h,g),(h,b,f),(g,f,c)][(x),(y),(z)]=

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  4. If A=[(1,-1),(2,-1)],B=[(x,1),(y,-1)] and (A+B)^(2)=A^(2)+B^(2) then (...

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  5. If alpha-beta=(2n+1)(pi)/2, n epsilon Z then [(cos^(2) alpha, cos alph...

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  6. If A=[(2,-2),(2,3)] and A^(2)-5A+kI(2)=0 then k =

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  7. If A=[(a,b),(c,d)],I=[(1,0),(0,1)] then A^(2)-(a+d)A=

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  8. If I = [(1,0),(0,1)] and E = [(0,1),(0,0)] then show that (aI + bE)^(3...

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  9. IF A=[{:(3,-4),(1,-1):}] then show that A^n=[{:(1+2n,-4n),(n,1-2n):}]...

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  10. if n is a positive integer and A=[(a,0,0),(0,b,0),(0,0,c)] then A^(n) ...

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  11. If A=((coshtheta,sinhtheta),(sinhtheta,coshtheta)) and ninN then A^(n)...

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  12. If A=[(1,1,0),(0,1,1),(0,0,1)] and ninN then A^(n)=

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  13. If A^(2)=2A-I then for n!=2,A^(n)=

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  14. If A=[(i,0,0),(0,i,0),(0,0,i)] then for ninN,A^(4n+1)=

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  15. If A=((0,0),(1,1)) then the value of A+A^(2)+A^(3)+ . . . .A^(n)=

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  16. If A=((2,-2,-4),(-1,3,4),(1,-2,k)) is an idempotent matrix then k =

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  17. IF A=[{:(2,4),(-1,k):}] and A^2=0 then find the value of k

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  18. A=[(1+i,2-3i,4),(7+2i,-i,3-2i)] then the conjugate of A is

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  19. If A is a skew-symmetric matrix and n is odd positive integer, then A^...

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  20. If [(1,-tan theta),( tan theta,1)][(1,tan theta),(-tan theta, 1)]^-1=[...

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