The effects of affine transformation [i]M[/i] on the square [i]BEAR [/i]and panda are depicted as [i]B'E'A'R[/i] .[br][br]Recall that the column vectors of the matrix [i]M[/i] are given by images [math]\vec{e}_1'[/math] , [math]\vec{e}_2'[/math] and [i]O'[/i] [br]where [math]\vec{e}_1=\begin{pmatrix}1\\0\end{pmatrix}[/math] and [math]\vec{e}_2=\begin{pmatrix}0\\1\end{pmatrix}[/math].[br][br]Manipulate with blue points [i]E1'[/i], [i]E2'[/i] and [i]O'[/i] to define a new affine transformation and see its corresponding matrix. You may also manipluate BE

[b]Exercises[/b][br][br]For the following four exercises, find the matrix for the linear transformation corresponding to[br][*] 1) scaling by the factor 1/2.[br][/*][*] 2) reflection across the line [math]y=-x[/math].[br][/*][*] 3) 180 degree rotation about the origin.[br][/*][*] 4) projection onto the [math]y[/math]-axis.[br][br]For the next four exercises, describe the transformation where the linear part is given by the matrix[br][/*][*] 1) [math]\begin{bmatrix}0 & -1\\1 & 0\end{bmatrix}[/math][br][/*][*] 2) [math]\begin{bmatrix}0.5 \quad 0.5\\0.5 \quad 0.5\end{bmatrix}[/math][br][/*][*] 3) [math]\begin{bmatrix}0 \quad 1\\1 \quad 0\end{bmatrix}[/math][br][/*][*] 4} [math]\begin{bmatrix}0 \quad 2\\2 \quad 0\end{bmatrix}[/math][br][/*]