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Math Help - det

  1. #1
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    det

    if det(A)=1 what is det(-2A) ? shouldn't it be -2, or am I totally lost on this one?
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  2. #2
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    I believe this is what you need to know:

    If a is a constant and A an nn square matrix, then |aA|=a^n|A|.

    Thus, det(-2A) = (-2)^n \times det(A). So it depends on the size of your matrix - if it's, say, a 2 x 2 matrix, then

    det(-2A) = (-2)^2 \times det(A) = 4 \times 1 = 4.

    Make sure to use the size of your matrix for n.

    (This is result 11 here: Determinant -- from Wolfram MathWorld. I actually don't recall this particular result, so there may be another method, particularly if you don't know the size of the matrix.)
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  3. #3
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    Quote Originally Posted by weasley74 View Post
    if det(A)=1 what is det(-2A) ? shouldn't it be -2, or am I totally lost on this one?
    det(-2A)=(-2)^2det(A) \Rightarrow 4

    This assumes it is a 2x2 matrix. If it is a 3x3 matrix, then you need to take negative two to the third power and so forth...

    EDIT: Not the first reply! Great explanation above!
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