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    Hi,

    For the attached question, I worked out that to calculate the area to T I would need to multiply the area of R by the determent of A to the power of 4. I got the right answer, but I was wondering how does this work - why am I able to do this?

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    Imagine a unit square on the coordinate plane. When you apply the 2*2 matrix 2 0 0 2 ( read left to right, top to bottom), you double the length of each side of the square because you are applying an enlargement of scale factor 2 about the origin.
    The determinant of this matrix is (2*2)-(0*0)=4. This is also the area scale factor increase as your 1*1=1 units^2 square has been enlarged to a 2*2=4 units^2 square.
    In this situation the matrix B is the same as applying A four times in a row so the scale factor increase is 2*2*2*2 =16 for B.

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    (Original post by FailedPolymath)
    Imagine a unit square on the coordinate plane. When you apply the 2*2 matrix 2 0 0 2 ( read left to right, top to bottom), you double the length of each side of the square because you are applying an enlargement of scale factor 2 about the origin.
    The determinant of this matrix is (2*2)-(0*0)=4. This is also the area scale factor increase as your 1*1=1 units^2 square has been enlarged to a 2*2=4 units^2 square.
    In this situation the matrix B is the same as applying A four times in a row so the scale factor increase is 2*2*2*2 =16 for B.

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    Thanks!


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