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Let a ,b , c be real numbers. The follow...

Let `a ,b , c` be real numbers. The following system of equations in `x ,y ` and `z` `(x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(a^2)=1,(x^2)/(a^2)-(y^2)/(b^2)+(z^2)/(a^2)=1,-(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(a^2)=1` has a. no solution b. unique solution c. infinitely many solutions d. finitely many solutions

A

no solution

B

unique solution

C

infinitely many solutions

D

finitely many solutions

Text Solution

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The correct Answer is:
b
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Chapter Test
  1. If A+B={:[(1,0),(1,1)]:}andA-2B={:[(-1,1),(0,-1)]:}, then A is equal t...

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  2. {:[(-6,5),(-7,6)]^(-1)=:}

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  3. From the matrix equation AB=AC, we conclude B=C provided.

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  4. If I3 is the identily matrix of order 3, then (I3)^(-1)=

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  5. Let a ,b , c be real numbers. The following system of equations in x ,...

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  6. If A and B are two matrices such that A+B and AB are both defind, then

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  7. A and B are tow square matrices of same order and A' denotes the tran...

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  8. STATEMENT-1: The lines a(1)x+b(1)y+c(1)=0a(2)x+b(2)y+c(2)=0,a(3)x+b(3)...

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  9. The system of linear equations x+y+z=2,2x+y-z=3, 3x+2y+kz=4 has a uniq...

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  10. If A and B ar square matrices of order 3 such that |A|=-1|B|=3, then |...

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  11. If the points (x1,y1),(x2,y2)and(x3,y3) are collinear, then the rank o...

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

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  13. Let A=[(0,0,-1),(0,-1,0),(-1,0,0)] Then only correct statement about t...

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  14. If {:A=[(1,2,2),(2,3,0),(0,1,2)]and adjA=[(6,-2,-6),(-4,2,x),(y,-1,-1)...

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  15. If A is a square matrix such that A*(AdjA)=[{:(4,0,0),(0,4,0),(0,0,4):...

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  16. If n is a natural number. Then {:[(2,-1),(3,-2)]^n:}, is

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  17. Given x=cy+bz,y=az+cx and that a^(2) +b^(2) +c^(2) +2abc =1.

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  18. If A is a singular matrix, then A (adj A) is a

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  19. If {:A=[(0,1),(1,0)]:},I is the unit matrix of order 2 and a, b are a...

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  20. If {:A=[(cos theta,-sintheta),(sintheta,costheta)]:}, then which one o...

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