Question

Use matrix multiplication to find the reflection of v(-1,2) about the line y=x

Answer 1

let the matrix be
\[\left[\begin{matrix}0 & 1 \\ 1 & 0\end{matrix}\right]\]
then...

Answer 2

In general the reflection matrix about the line that forms angle alph with x axis is:\[A=\left[\begin{matrix}\cos2\alpha & \sin2\alpha\\ \sin2\alpha& -\cos2\alpha\end{matrix}\right]\]
Hope this helps

Answer 3

thanks for all but i know that ,idont how to use it ? if you can help me

Answer 4

y=x forms an 45º angle with x axis. So cos90º = 0,sin90º=1
substitute this into A and you got it

Answer 5

thanks myko

Answer 6

\[reflection= \left[\begin{matrix}0 & 1 \\ 1 & 0\end{matrix}\right]\left(\begin{matrix}-1\\ 2\end{matrix}\right)\]

Answer 7

can you help me for (2,-5,3) please myko,and thanks for you

Answer 8

(2,-5,3)?

Answer 9

matrix multiplication to find the reflection of v=(2@-5@3)
about the xz-plane

Answer 10

General formula for reflection about ax+by+cz=0 plane is
\[A=\left[\begin{matrix}1-2a ^{2} & -2ab & -2ac\\ -2ab & 1-2b ^{2}& -2bc \\-2ac & -2bc&1-2c ^{2}\end{matrix}\right]\]
Can you find out by your self the equation of you plane and substitute values in the matrix?

Answer 11

ok, equation of xz plane is y=0. So a=0, b=1,c=0. Just put this into the matrix and do like befor

Answer 12

@m.f.h

Answer 13

thanks for u myko