For the linear transformation & represented by the equation x - 2y = 0, find a vector v parallel to e, and a vector w perpendicular to l. Make your vectors v and w simple so that your computations are not overly complicated. Determine the matrix Au for the reflection on l with respect to the ordered basis U == {v, w}. Finally use the appropriate transition matrices to compute the standard matrix representation A of l with respect to the standard basis. Use the standard matrix representation to find the reflections of the points (2, 1), (−1, 2), and (5,0) with respect to l.

Find the matrix A of the linear transformation T from R2 to R² that rotates any vector through an angle of 150° in the clockwise direction. A =

Let T : R2 → R² be the linear transformation which rotates vectors counter-clockwise about the origin by 7T/3 radians (60 degrees). (i) Find the standard matrix of the linear transformation T. (ii) Use your matrix to rotate the vector v = counterclockwise about the origin by 4 T/3 radians.

The cross product of two vectors in R³ is defined by Let ✓ = A = [1] 8 . Find the matrix A of the linear transformation from R³ to R³ given by T(x) = × đ. a2 X b₁ b₂ b3 = [a2b3-a3b₂] | a3b1 — a1b3 [a1b₂-a2b₁]