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Show that |{:(1,a,a^2),(1 ,b,b^2),(1,c,...

Show that `|{:(1,a,a^2),(1 ,b,b^2),(1,c,c^2):}|`=(a-b)(b-c)(c-a)

Answer

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S.T |(1,a,a^2),(1,b,b^2),(1,c,c^2)| = (a-b)(b-c)(c-a) .

Show that |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}| =(a-b)(b-c)(c-a)(ab+bc+ca)

Knowledge Check

  • If Delta=|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=k(a-b)(b-c)(c-a) then k=

    A
    abc
    B
    0
    C
    1
    D
    -1

  • |(1,a,a^(2)+bc),(1,b,b^(2)+ac),(1,c,c^(2)+ab)|=k(a-b),(b-c), (c-a) then k =

    A
    2
    B
    `-2`
    C
    1
    D
    `-1`

    • Similar Questions

    Explore conceptually related problems

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    Show that |{:(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab):}|=0

    Show that |{:(bc,b-c,1),(ca,c+a,1),(ab,a+b,1):}|=(a-b)(b-c)(c-a)

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    Show that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3

    Without expanding the determinant , prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

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