Final answer:
The matrix that represents a clockwise rotation around the origin by π/3 is [1/2 -√3/2 √3/2 1/2]. The matrix that represents a clockwise rotation followed by a projection onto the x-axis is [1/2 0 √3/2 0].
Step-by-step explanation:
To find the matrix that represents a rotation clockwise around the origin by π/3, we can use the following formula:
R = [cos(θ) -sin(θ)
sin(θ) cos(θ)]
Substituting θ = π/3 into the formula, we get:
R = [cos(π/3) -sin(π/3)
sin(π/3) cos(π/3)]
Simplifying, we have:
R = [1/2 -√3/2
√3/2 1/2]
To find the matrix that represents a rotation clockwise around the origin by π/3 followed by a projection onto the x-axis, we can multiply the rotation matrix by the projection matrix [1 0
0 0].
Multiplying the matrices, we have:
R * P = [1/2 -√3/2 * 1 0
√3/2 1/2 * 0 0]
Simplifying, we get:
R * P = [1/2 0
√3/2 0]