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Math Help - how to find area of figure if given Linear Operator Matrix

  1. #1
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    how to find area of figure if given Linear Operator Matrix

    Let a Linear operator on \Re^2 have the following matrix:

    A = \begin{pmatrix}<br />
1 & 0\\<br />
-1 &3<br />
\end{pmatrix}

    What is the area of the figure that results from applying this transformation to the unit square?
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  2. #2
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    Quote Originally Posted by r2dee6 View Post
    Let a Linear operator on \Re^2 have the following matrix:

    A = \begin{pmatrix}<br />
1 & 0\\<br />
-1 &3<br />
\end{pmatrix}

    What is the area of the figure that results from applying this transformation to the unit square?
    the area = |\det A| \cdot (\text{the area of the unit square})=3.
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