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If a, b and c are real numbers, and Delt...

If a, b and c are real numbers, and `Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]|=0`. Show that either `a+b+c=0` or `a=b=c`

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CENGAGE ENGLISH-DETERMINANTS-All Questions
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  2. Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(x-...

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  3. If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c]...

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  4. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

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  5. Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)...

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  6. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b]...

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  7. Using the properties of determinants, prove that following |(a-b-c,2a,...

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  8. If a1,a2,a3,.....an.... are in G.P. then the determinant 'Delta=|[loga...

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  9. Using properties of determinants, prove the following |(a^2,ab,ac),(ab...

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  10. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually perp...

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  11. The number of distinct real roots of |[sinx,cosx,cosx],[cosx,sinx,cosx...

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

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  13. If lines p x+q y+r=0,q x+r y+p=0 and r x+p y+q=0 are concurrent, the...

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  14. If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-...

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  15. Find the value of lambdaif2x^2+7x y+3y^2+8x+14 y+lambda=0 represent a ...

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  16. If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b...

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  17. If A , B ,C are angles of a triangle, then the value of |[e^(2i A),e^(...

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  18. If a^2+b^2+c^2=1, then prove that |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ...

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  19. For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, There are exa...

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  20. Let Deltar=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]|. Sho...

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