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The determinants |(1,a,bc),(1,b,ca),(1,c...

The determinants `|(1,a,bc),(1,b,ca),(1,c,ab)| and |(1,a,a^2),(1,b,b^2),(1,c,c^2)|` are identically equal.

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Explore conceptually related problems

The determinants |{:(1,a, bc),(1, b, ca),(1, c, ab):}| " and "|{:(1,a, a^(2)),(1, b, b^(2)),(1, c, c^(2)):}| are not identically equal.

Prove that |[1,a,bc] , [1,b,ca], [1,c,ab]|=|[1,a,a^2] , [1,b,b^2] , [1,c,c^2]|

Knowledge Check

  • Consider the following statements : 1. The determinants |(1,a,bc),(1,b,ca),(1,c,ab)| and |(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))| are not identically equal. 2. For a gt 0, b gt 0, c gt 0 the value of the determinant |(a,b,c),(b,c,a),(c,a,b)| is always positive. 3. If |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|=|(a_(1),b_(1),1),(a_(2),b_(2),1),(a_(3),b_(3),1)| , then the two triangles with vertices (x_(1),y_(1)), (x_(2),y_(2)), (x_(3), y_(3)) and (a_(1),b_(1)), (a_(2), b_(2)), (a_(3), b_(3)) must be congruent. Which of the statement given above is/are correct?

    A
    Only (1)
    B
    Only (2)
    C
    Only (3)
    D
    None of these

  • |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| =

    A
    abc
    B
    `a^2b^2c^2`
    C
    0
    D
    none

  • |(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab)|=

    A
    abc
    B
    `1/(abc)`
    C
    `ab+bc+ca`
    D
    0

    • Similar Questions

    Explore conceptually related problems

    1,bc,b+c1,ca,c+a1,ab,a+b]|=det[[1,a,a^(2)1,b,b^(2)1,c,c^(2)]]

    det[[1,a,a^(2)+bc1,b,b^(2)+ac1,c,c^(2)+ab]] is equal to

    Delta=det[[1,a,bc1,b,ca1,c,ab]]

    The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^2) (B) a^3+b^3+c^3-3abc (C) (a-b)(b-c)(c-a) (D) 0

    (1)/(a),a^(2),bc(1)/(b),b^(2),ca(1)/(c),c^(2),ab]|

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