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Consider the system of the equation k x+...

Consider the system of the equation `k x+y+z=1,x+k y+z=k ,a n dx+y+k z=k^2dot` Statement 1: System equations has infinite solutions when `k=1.` Statement 2: If the determinant `|1 1 1k k1k^2 1k|=0,` t hen `k=-1.`

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CENGAGE-DETERMINANTS-All Questions
  1. Consider the determinant f(x)=|0x^2-a x^3-b x^2+a0x^2+c x^4+b x-c0|dot...

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  2. Find the value of |1 2 4-1 3 0 4 1 0|

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  3. Consider the system of the equation k x+y+z=1,x+k y+z=k ,a n dx+y+k z=...

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  4. Each question has four choices a, b, c and d, out of which only one is...

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  5. If a ,b ,c in R , then find the number of real roots of the equat...

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  6. Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)| is divisible by ...

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  7. Without expanding at any stage, prove that the value of each of the...

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  8. If a,b,c are all positive, and are p^(th), q^(th) and r^(th) terms of ...

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  9. If the entries in a 3xx3 determinant are either 0 or 1, then the grea...

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  10. The value of the determinant of n^(t h) order, being given by |x1 11x1...

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  11. Solve the equation {:[( x+a,x,x),(x,x+a,x),(x,x,x+a) ]:}=0,ane 0

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  12. If a1b1, c1,a2b2c2a n da3b3c3 are three digit even natural numbers and...

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  13. If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ...

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  14. The value of |[yz, z x,x y],[ p,2q,3r],[1, 1, 1]|,w h e r ex ,y ,z are...

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  15. Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+...

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  16. If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0, then ...

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  17. If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, th...

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  18. Prove that |{:(2,,alpha+beta+gamma+delta,,alphabeta+gammadelta),(alpha...

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  19. Solve for x ,|x-6-1 2-3xx-3-3 2xx+2|=0.

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  20. The value of determinant |1 1 1^m C1^(m+1)C1^(m+2)C1^m C2^(m+1)C2^(m+2...

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