Rotating Linear

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October 4th, 2007 admin Leave a comment Go to comments

Rotating Linear

Vector Rotated Linear Algebra Question?

Does anyone have a good explanation to this problem? Thanks
Consider a vector (x,y) in R2 that is rotated 45 degrees clockwise, then reflected across the y axis, then projected on the x axis.
A) Find the matrix of T= T3 * T2 * T1 which accomplishes this.
B) Find the ker(T).

T1 will be the rotation matrix (note the minus sign, since the rotation is clockwise)
[ cos(-45) -sin(-45)] =
[ sin(-45) cos(-45)]

[1 1] * sqrt(2/2).
[-1 1]

T2 will be the reflection matrix
[1 0]
[0 -1]
(since T2(1,0) = (1,0) and T2(0,1) = (0,-1).)

T3 will be the projection matrix
[1 0]
[0 0]
(since T3(1,0) = (1,0) and T3(0,1) = (0,0).)

I’ll leave it to you to multiply these to get T.

As for Part B), just row reduce and set the matrix equal to the zero vector. Good luck!

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