A bit lost in doing this and unsure of my answers can someon

A bit lost in doing this, and unsure of my answers, can someone show work for these

Find the matrix of following transformations:

1 .) Rotation of vectors in iR^2 by 60 degrees counter clockwise

2.) Reflection of points in iR^2 across line y=-x

3.) Multiplication of the point (x,y,z) in iR^3 to give the point (x+y, y, x+z)

Solution

Answer 1

The standard matrix of rotation by angle \'a\' is

[ cos(a) -sin(a) ]
[ sin(a)   cos(a) ]

Here given that a= 60 degree.

Answer 2

If we reflect points (x,y) over the line y = -x,
the x-coordinate and y-coordinate change places and the signs are changed.

The reflection of the point (x,y) across
the line y = -x is the point (-y, -x).