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If |b+c c+a a+b a+b b+c c+a c+a a+b b+c|...

If `|b+c c+a a+b a+b b+c c+a c+a a+b b+c|=k|ab c c a b b c a|` , then value of `k` is `1` b. `2` c. `3` d. `4`

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. If a ,b ,c are different, then the value of |[0,x^2-a, x^3-b],[ x^2+a,...

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

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  3. If |b+c c+a a+b a+b b+c c+a c+a a+b b+c|=k|ab c c a b b c a| , then va...

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

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  5. If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,b...

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

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  7. Prove that the value of each the following determinants is zero: |[(a^...

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  8. 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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  9. Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2...

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  10. Prove that the value of each the following determinants is zero: |[l...

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  11. 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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  12. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|= 1

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  13. The determinant |a b aalpha+bb c balpha+c aalpha+bbalpha+c0|=0, if a ...

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  14. By using properties of determinants. Show that: |1+a^2-b^2 2a b-2b2a b...

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  15. Which of the following values of alpha satisfying the equation |(1+alp...

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  16. Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b...

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  17. If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite s...

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  18. If |[6i,-3i,1],[ 4, 3i,-1],[ 20, 3,i]|=x+i y , then a.x=3,y=1 b. x=1,y...

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  19. The value of |[yz, z x,x y],[ p,2q,3r],[1, 1, 1]| , where x ,y ,z are ...

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  20. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

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