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Value of [[x+y, z,z ],[x, y+z, x],[y, y,...

Value of `[[x+y, z,z ],[x, y+z, x],[y, y, z+x]],` where x ,y ,z are nonzero real number, is equal to `x y z` b. `2x y z` c. `3x y z` d. `4x y z`

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CENGAGE-DETERMINANTS-All Questions
  1. Let x<1, then value of [[x^2+2, 2x+1 ,1],[ 2x+1,x+2, 1],[ 3, 3 ,1]...

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  2. If f (x) = |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|then

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  3. Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are non...

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  4. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

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  5. If A,B,C are the angles of a non right angled triangle ABC. Then find ...

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  6. If f(x)=|x a a a x a a a x|=0, then f^(prime)(x)=0a n df^(x)=0 has com...

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  7. Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),...

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  8. Roots of the equation |x m n1a x n1a b x1a b c1|=0 are independent of ...

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  9. Prove that the value of determinants is zero: |a-b b-c c-a x-y y-z ...

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  10. If a ,b ,c are different, then the value of |0x^2-a x^3-b x^2+a0x^2+c ...

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  11. Prove that the value of each the following determinants is zero: |...

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  12. If |b+cc+a a+b a+bb+cc+a c+a a+bb+c|=k|a b cc a bb c a| , then value o...

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  13. A triangle has vertices Ai(xi , yi)fori=1,2,3 If the orthocentre of tr...

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  14. If alpha,beta,gamma are the roots of a x^3+b x^2+c x+d=0a n d|alpha ...

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  15. If Delta=|(a1,b1,c1),(a2,b2,c2),(a3,b3,c3)| and Delta1=|(a1+pb1,b1+q...

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  16. Prove that the value of each the following determinants is zero: |...

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  17. The value of the determinant [(1^2, 2^2, 3^2, 4^2) ,(2^2, 3^2 ,4^2,5^2...

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  18. If f(x)=|1x x+1 2x x(x-1)(x+1) x3 x(x-1) x(x-1)(x-2) (x+1)x(x-1)| then...

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  19. Show that |(log x, log y, logz),(log 2x, log2y, log2z),(log3x, log3y,l...

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  20. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

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