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The system of linear equations x+lambday...

The system of linear equations `x+lambday-z=0`, `lambdax-y-z=0`, `x+y-lambdaz=0` has a non-trivial solution for : (1) infinitely many values of `lambda` . (2) exactly one value of `lambda` . (3) exactly two values of `lambda` . (4) exactly three values of `lambda` .

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...

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  2. If xi=ai bi ci,i=1,2,3 are three-digit positive integer such that ea...

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  3. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

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  4. If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^...

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  5. If p q r!=0 and the system of equation (p+a)x+b y+c z=0, a x+(q+b)y+c...

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  6. If c<1 and the system of equations x+y-1=0,2x-y-c=0,a n d -b x+3b y-c=...

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  7. Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(...

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

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

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

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  13. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[log a...

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  14. Prove that,abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1))=1+a^2+b^2+c^...

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

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  16. The number of distinct roots of abs((sinx, cosx, cosx),(cosx, sinx, co...

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

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

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

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