曲线y=log2x在M=0110作用下变换的结果是曲线方程______.

曲线y=log2x在M=0110作用下变换的结果是曲线方程______.

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曲线y=log2x在M=



01
10



作用下变换的结果是曲线方程______.
答案
设P(x,y)是曲线y=log2x上的任一点,
P1(x′,y′)是P(x,y)在矩阵 M=



01
10



对应变换作用下新曲线上的对应点,



x′
y′



=



01
10






x
y



=



y
x



(3分)





x′=y
y′=x
,所以





x=y′
y=x′
,(6分)





x=y′
y=x′
代入曲线y=log2x,得x′=log2y′,(8分)
即y′=2x′
曲线y=log2x在M=



01
10



作用下变换的结果是曲线方程 y=2x
故答案为:y=2x
举一反三
若矩阵A=是表示我校2011届学生高二上学期的期中成绩矩阵,A中元素aij(i=1,2,3,4;j=1,2,3,4,5,6)的含义如下:i=1表示语文成绩,i=2表示数学成绩,i=3表示英语成绩,i=4表示语数外三门总分成绩j=k,k∈N*表示第50k名分数.若经过一定量的努力,各科能前进的名次是一样的.现小明的各科排名均在250左右,他想尽量提高三门总分分数,那么他应把努力方向主要放在哪一门学科上(  )
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A.语文B.数学C.外语D.都一样
把矩阵data:image/png;base64,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变为data:image/png;base64,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后,与对应的值是(  )
A.
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规定运算
.
ab
cd
.
=ad-bc
,则
.
1i
-i2
.
=______.
选修4-2:矩阵与变换
已知矩阵M=



01
10



N=



0-1
10



.在平面直角坐标系中,设直线2x-y+1=0在矩阵MN对应的变换作用下得到曲线F,求曲线F的方程.
A=



13
24



,B=



-12
3-3



,则3A-B=______.