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Show that |(log x, log y, logz),(log 2x,...

Show that `|(log x, log y, logz),(log 2x, log2y, log2z),(log3x, log3y,log3z)|=0`

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The value of the determinant |[log_a(x/y), log_a(y/z), log_a(z/x)], [log_b (y/z), log_b (z/x), log_b (x/y)], [log_c (z/x), log_c (x/y), log_c (y/z)]|

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CENGAGE-DETERMINANTS-All Questions
  1. 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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  2. If f(x)=|1x x+1 2x x(x-1)(x+1) x3 x(x-1) x(x-1)(x-2) (x+1)x(x-1)| then...

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  3. Show that |(log x, log y, logz),(log 2x, log2y, log2z),(log3x, log3y,l...

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  4. 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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  5. {:[( 1,1+p,1+p+q),( 2,3+2p,4+3p+2q),( 3,6+3p,10+6p+3q)]:}=1

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  6. If |(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0)|=0, prove that...

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

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  8. Which of the following values of alpha satisfy the equation |{:((...

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  9. solve {:[( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) ]:} = 3( a+...

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  10. 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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  11. \begin{bmatrix}6i&-3i&1\\ 4 &3i& -1\\ ...

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

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

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  15. The number of values of k for which the lines (k+1)x+8y=4k a n dk x+(k...

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  16. Prove that |b+c a-b a c+a b-c b a+b c-a c|=3a b-a^3-b^3-c^3dot

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  17. If |a^2b^2c^2(a+1)^2(b+1)^2(c+1)^2(a-1)^2(b-1)^2(c-1)^2|=k(a-b)(b-c)(c...

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  18. Statement 1: "Delta"=|m y+n z m q+n r m b+n c k z-m x k r-m p k c-m a-...

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  19. Prove that =|1 1 1 a b c b c+...

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  20. If the determinant ∣ cos(θ+ϕ) sinθ −cosθ ​−sin(θ+ϕ) cosθ sinθ cos2ϕ ...

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