题目内容
(选修4—2 矩阵与变换)(本题满分7分)
变换
是将平面上每个点
的横坐标乘2,纵坐标乘4,变到点
。
(Ⅰ)求变换
的矩阵;
(Ⅱ)圆
在变换
的作用下变成了什么图形?
变换



(Ⅰ)求变换

(Ⅱ)圆


(Ⅰ)
(Ⅱ)变成了椭圆


本试题主要是考查了矩阵的运算,以及图像的变换的综合运用。
(1)由已知得
,因此变化T的矩阵是
(2)由
,得:
,代入方程
中得到结论。
解: (1)(选修4—2 矩阵与变换)(本题满分7分)
(Ⅰ)由已知得
变化T的矩阵是
…………3分
(Ⅱ)由
,得:
,
代入方程
,得:
∴圆C:
在变化T的作用下变成了椭圆
…………7分
(1)由已知得


(2)由



解: (1)(选修4—2 矩阵与变换)(本题满分7分)
(Ⅰ)由已知得



(Ⅱ)由


代入方程


∴圆C:



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