# Thread: how to find area of figure if given Linear Operator Matrix

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

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

A = $\begin{pmatrix}
1 & 0\\
-1 &3
\end{pmatrix}$

What is the area of the figure that results from applying this transformation to the unit square?

2. Originally Posted by r2dee6
Let a Linear operator on $\Re^2$ have the following matrix:

A = $\begin{pmatrix}
1 & 0\\
-1 &3
\end{pmatrix}$

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