Final answer:
To find the matrix of a linear transformation that rotates a 2-vector clockwise by π/6 in homogeneous coordinates in R^3, we can use the rotation matrix formula.
Step-by-step explanation:
In order to find the matrix of a linear transformation that rotates a 2-vector clockwise by π/6 in homogeneous coordinates in R3, we can use the rotation matrix formula.
Let's consider a 2D vector in homogeneous coordinates, (x,y,1).
The rotation matrix for rotation by π/6 in the counterclockwise direction can be written as:
R = [[cos(π/6), -sin(π/6), 0], [sin(π/6), cos(π/6), 0], [0, 0, 1]]
Now, we can apply this rotation matrix to the given 2-vector to obtain the matrix of the linear transformation:
T = [[cos(π/6), -sin(π/6), 0], [sin(π/6), cos(π/6), 0], [0, 0, 1]] * [[x], [y], [1]]
Simplifying the multiplication gives us the resulting matrix.