Final answer:
The standard matrix A for a clockwise rotation of 60° in R2 is a 2x2 matrix with the values [[0.5, 0.866], [-0.866, 0.5]].
Step-by-step explanation:
The student is asking for the standard matrix A of a linear transformation T, which represents a clockwise rotation of 60° in the plane R2. Since the rotation is clockwise and given by a negative angle in conventional mathematical notation (counter-clockwise is positive), we're looking at a rotation of -60°. The standard matrix A for a rotation by theta in the plane is:
[ cos(theta) -sin(theta)]
[sin(theta) cos(theta)]
For a -60° rotation, the matrix becomes:
[ cos(-60°) -sin(-60°)]
[sin(-60°) cos(-60°)]
Substituting the values, we have:
[ 0.5 0.866]
[-0.866 0.5 ]
This represents the standard matrix A for the rotation transformation T.