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Math Help - condition for linearly dependent

  1. #1
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    condition for linearly dependent

    Let
    U=a₁I+b₁X+c₁Y+d₁XY
    V=a₂I+b₂X+c₂Y+d₂XY
    W=a₃I+b₃X+c₃Y+d₃XY
    Now if I,U,V, and W are linearly dependent, then how we can write
    det of matrix

    b₁ c₁ d₁
    b₂ c₂ d₂
    b₃ c₃ d₃
    =0, plz explain
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  2. #2
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    Quote Originally Posted by maken83 View Post
    Let
    U=a₁I+b₁X+c₁Y+d₁XY
    V=a₂I+b₂X+c₂Y+d₂XY
    W=a₃I+b₃X+c₃Y+d₃XY
    Now if I,U,V, and W are linearly dependent, then how we can write
    det of matrix

    b₁ c₁ d₁
    b₂ c₂ d₂
    b₃ c₃ d₃
    =0, plz explain
    The det of a matrix is zero if any two or more rows are multiples of each other or if there is a row or column of all zeros.

    What does the def of lin. dep. say?
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