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The determinant: |(xp+y,x,y),(yp+z,y,z...

The determinant:
`|(xp+y,x,y),(yp+z,y,z),(0,xp+y,yp+z)|=0` if :

A

`x, y, z` are in A.P

B

`x, y, z` are in G.P.

C

x, y, z` are in H.P

D

`x y, y z, z x` are in A.P

Text Solution

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The correct Answer is:
B
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HIMALAYA PUBLICATION-MATRICES AND DETERMINANTS-QUESTION BANK
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  2. If 3^n is a factor of the determinant [[1,1,1],[n C(1),(n+3) C(1) ,(n+...

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  3. The determinant: |(xp+y,x,y),(yp+z,y,z),(0,xp+y,yp+z)|=0 if :

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  4. If f(x)=[[1 ,x ,x+1],[2 x ,x(x-1) ,(x+1) x],[3 x(x-1),x(x-1)(x-2) ,...

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  5. If A=[[alpha , 0] ,[ 1 , 1]] and B=[[1 , 0] ,[ 5 , 1]] whenever A^(2)=...

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  6. If A=[[a , b] ,[ b , a]] A^(2)=[[alpha , beta] ,[ beta , a]] then

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  7. Let A = [(1,-1,1),(2,1,-3),(1,1,1)] and (10)B = [(4,2,2),(-5,0,alpha),...

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  8. Let A=[[0, 0 ,-1],[0,-1,0],[-1,0,0]]. The only correct statement about...

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  9. If A+B are square matrices of size nxxn such that A^(2) - B^(2) = (A-...

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  10. Let A = ((1,2),(3,4)) and B = ((a,0),(0,b)), a b in N . Then :

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  11. Let A= [[5,5 alpha, alpha],[0 ,alpha,5 alpha ],[0,0,5]] |A^(2)|=25, t...

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  12. Let A = [[1,2],[0,1]]. Then A^(n) =

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  13. If [[2+x,3,4],[1,-1,2],[x,1,-5]] is singular matrix then x is

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  14. For the matrix A=[[1,1,0],[1,2,1],[2,1,0]] which is correct?

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  15. If A^(2) - A + I = O , then the inverse of A is :

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  16. If P= [[i,0,-i],[0,-i,i],[-i,i,0]], Q= [[-i,i],[0,0],[i, -i]] then P Q...

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  17. If A= [[2,-1],[-1,2]] and I is the unit matrix of order 2 , then A^2 i...

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  18. Let X= [[x1],[x2],[x3]], A= [[1,-1,2],[2,0,1],[3,2,1]] and B= [[3],[1]...

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  19. Let X= [[x],[y],[z]], D= [[3],[5],[11]], A= [[1,-1,2],[2,1,1],[4,-1,-2...

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  20. If X=[[1,1],[1,1]], then X^n, for n in N is equal to

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