Question

Find the matrix of a linear transformation in R3 in homo coordinates that rotates a 2 vector clockwise by pi/6

Answer 1

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.