Matricy Transformations

Question 1

Rotation matrix (anti Louise through angle theta)

Answer 1

Derrive by transforming identity to through theta

Becomes

Cos x , -sinx
Sinx, cos x

Essentially leading diagonal is same and same sign
Other diagonal is same different sign= rotation Matrix

And aolve by equating cos x and sinx to relevant numbers.
And using CAST, find a SOLUTION THAT IS THE SAME FOR BOTH!

Remmeber the side LENTGH same thatshow to derrive

Question 2

Reflection matrix through angle theta or y= tan theta x

Answer 2

May not need to know

Question 3

How ti de shears

Answer 3

Apply the shear to a poijt x, y

You’ll see that each ooijt now has been TRASNAKTED (not stretch) by some factor kx , ky

However correvt way to define =
- say which line is CONSTANT)
- then say how one point is now another

This is the proper SPEC WAY OF DOUGH IT