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Math Help - Use properties of determinant

  1. #1
    Junior Member
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    Use properties of determinant

    The answer key says 8 but I'm getting 2. I think the problem is when I factor out the 1/2, should I be factoring out a 2 instead?

    Any help is appreciated!
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  2. #2
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    You made a very simple mistake.

    You have \det A = -4, -\frac{1}{2}\det B = -4.

    Therefore, \det B = -4 \cdot -2 = 8.
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  3. #3
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    Quote Originally Posted by icemanfan View Post
    You made a very simple mistake.

    You have \det A = -4, -\frac{1}{2}\det B = -4.

    Therefore, \det B = -4 \cdot -2 = 8.

    I still don't understand, isn't there the property:


    If B is the matrix that results when a single row or column of A is multiplied by a scalar k, then det(B)= kdet(A)


    If I were to multiply det(A) by k=1/2 then I would get det(B)

    So det(B)= kdet(A)

    Or is it that I'm just thinking of this all backwards?


    I know for sure that if (from another example) if I divided a row by some scalar k, say I divided by 2, I would have something like kdet(A) so then 2det(A)

    Thanks!
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  4. #4
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    Quote Originally Posted by DarK View Post
    I still don't understand, isn't there the property:


    If B is the matrix that results when a single row or column of A is multiplied by a scalar k, then det(B)= kdet(A)
    Precisely. The determinant of the matrix A before you multiplied one of the rows by 2 was 4. Hence the determinant of matrix B, which resulted from multiplying a row of A by 2, is 8.
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