矩阵与线性变换演示 iShow

Consider the unit square in the app above. If you consider the coordinates of its vertices, listed anticlockwise starting from the origin, you can form the coordinate matrix of the vertices: . Now select a Custom transformation, and set the two elements of the main diagonal of the transformation matrix equal to 2, and the remaining elements equal to 0. What transformation have you obtained? Compare the areas of the unit square and the transformed square. If you set the transformation matrix equal to , what would be the area of the transformed figure? Verify your conjecture by computing the coordinates of the vertices of the transformed figure, and determining its area. 考虑上面应用中的单位方形。如果你考虑其顶点的坐标，从原点逆时针排列，可以构造顶点的坐标矩阵： 。 现在选择一个自定义变换，将变换矩阵主对角线的两个元素设为 2，其余元素为 0。 你获得了什么变身？ 比较单位正方形和变换后的正方形的面积。 如果你将变换矩阵设为 ，变换后图形的面积会是多少？ 通过计算变换图形顶点的坐标并确定其面积来验证你的猜想。

The list of transformations available in the app doesn't include reflection about the origin. Can you obtain this transformation using one of the available options? Explain your answer in detail. 应用中可用的变形列表中没有关于起源的反射 。 你能通过现有选项之一实现这种变身吗？ 请详细解释你的回答。