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If |(b +c,c +a,a +b),(a +b,b +c,c +a),(c...

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

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

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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 |(a,b,c),(...

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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. If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f...

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

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

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  15. 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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  16. 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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  17. 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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  18. The value of |y z z xx y p2p3r1 1 1|,w h e r ex ,y ,z are respectively...

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

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

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