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Let a, b, c be any real numbers. Supp...

Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that `x""=""c y""+""b z ,""y""=""a z""+""c x""a n d""z""=""b x""+""a y` . Then `a^2+""b^2+""c^2+""2a b c` is equal to (1) 2 (2) `""1` (3) 0 (4) 1

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ALLEN-DETERMINANTS-All Questions
  1. The value of |alpha| for which the system of equation alphax+y+z=alpha...

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  2. If D=|1 1 1 1 1+x1 1 1 1+y|"f o r"x!=0, y!=0 then D is (1) divisibl...

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  3. Let a, b, c be any real numbers. Suppose that there are real number...

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  4. Let a, b, c be such that b(a""+""c)!=0 . If |a a+1a-1-bb+1b-1cc-1c...

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  5. Consider the system of linear equations; x-1\ +2x2+x3=3 2x1+3x2+3=3 3x...

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  6. The number of value of k for which the linear equations 4x+k y+2z=0k x...

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  7. If the trivial solution is the only solution of the system of equation...

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  8. The number of values of k, for which the system of equations (k""+"...

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  9. If a ,b ,c are sides of a scalene triangle, then value of |a b c b c a...

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  10. If the system of linear equations x1+2x2+3x3=6,\ x1+3x2+5x3=9,\ 2x2+5x...

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  11. Statement 1: The system of linear equations x+(sinalpha)y+(cosalpha)z=...

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  12. Consider the system of equations x+a y=0,\ y+a z=0.\ Then the set of ...

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  13. If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)...

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  14. The set of all values of lamda for which the system of linear equation...

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  15. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambd...

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  16. The number of distinct real roots of the equation |cosx s in x s in x ...

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  17. Test the consistency and solve them when consistent the following s...

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  18. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

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  19. The number of values of k for which the system of the equations (k+1)x...

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  20. The value of lambda for which the system of equations 2x-y-z=12,x-2y +...

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