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If a , b , c are non-zero, then the syst...

If `a , b , c` are non-zero, then the system of equations `(alpha+a)x+alphay+alphaz=0,alphax+ , (alpha+b)y+alphaz=0,alphax+alphay+(alpha+c)z=0` has a non-trivial solution if `alpha^(-1)=` (A) ` -(a^(-1)+b^(-1)+c^(-1))` (B) `a+b+c` (C) `alpha+a+b+c=1` (D) none of these

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CENGAGE-DETERMINANTS-All Questions
  1. Prove that |(x^2,x^2-(y-z)^2,yz),(y^2,y^2-(z-x)^2,zx),(z^2,z^2-(x-y)^2...

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  2. If a,b and c are real numbers, and Delta ={:[( b+c,C+a,a+b),( c+a,a...

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

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  4. Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

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

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  6. If |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c) xx(x + a + b...

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  7. If a(1), a(2), a(3), ………, a(n)….. are in G.P., then the determinant De...

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  8. By using properties of determinants , show that : {:[( a^(2) + 1, a...

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

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

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

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  12. If lines p x+q y+r=0,q x+r y+p=0a n dr x+p y+q=0 are concurrent, th...

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

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  14. Find the value of lambda if 2x^2+7x y+3y^2+8x+14 t+lambda=0 represents...

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

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

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

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  18. Let "Delta"r=|r-1n6(r-1)^2 2n^2 4n-2(r-1)^2 3n^3 3n^2-3n|dot Show that...

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  19. Let m be a positive integer and Deltar=|[2r-1,.^mCr,1],[m^2-1,2^m,m+1]...

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  20. Prove that |1+a 1 1 1 1 1+b 1 1 1 1 1+c ...

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