!! used as default html header if there is none in the selected theme. Linear shoot

# Linear shoot --- Introduction ---

This is a visual exercise on the linear transformation in dimension 2: let $M=\left(\begin{array}{cc}a& b\\ c& d\\ \end{array}\right)$ be a 2×2 matrix. Then $M$ corresponds to a linear transformation of ${ℝ}^{2}$: for any point $p=\left(\begin{array}{c}x\\ y\end{array}\right)\in {ℝ}^{2}$, the image of $p$ by the linear transformation is the point $q=Mp=\left(\begin{array}{c}ax+by\\ cx+dy\end{array}\right)$.

Now the exercise gives you the matrix $M$ , numerically described, as well as a figure representing the point $p$ in the cartesian plane. You are simply asked to click (shoot) on where you think is the position of the image point $q$. At the end of a session composed of several shots, you will be given a score computed according to the average precision of your shots during the session.

Choose a level of difficulty : 1 , 2 , 3 , 4 , 5 , 6 , 7 .

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• Description: click on the image of a point by a linear transformation. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games
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