Can you also provide me with a proof for the matrix of the rotation function T:R2->R2?
Find the matrix of the composition SoT' and decide whether it is a reflection or a rotation If it is a rotation then find the angle of rotation; if it is a reflection, then find the angle between the positive x-axis and the line of reflection. (a) T : R2-> R2 by angle /6 about the origin, and S:R2-R2 is the reflection in the line L, given by the equation y--v3x (b) T: R2R2 is the reflection in the line L passing through the origin and the first quadrant, making angle Ï/8 with the x-axis, and S : R2-> R2 is the (counter-clockwise) rotation by angle 11T/6 about the origin s the counter-clockwise) rotation Let Î be a plane in Rn passing through the origin, and parallel to some vectors a, b E Rn. Then the set V. of position vectors of points of 11, is given by V jua+ vb , v e R} Prove that V is a subspace of Rn.
