Give the associated matrix of a transformation on R² that performs the following: A reflection about the x axis followed by Counterclockwise rotation through by an angle 0 = 150⁰ a. بر أن الله ان 1 √3 NIN NEW N b. W/W N/N √3 2 1 C. √√3 2 N N/W NIN √3 d. √3 2 -|~ 27/12 NEW NIN √3

Construct a homogeneous transformation matrix with the provided rotation and translations. R 7 Hint: Remember that a homogeoneous matrix looks like 0 1

Only (a) and (d) and (e).

36. (a) What matrix transforms (1,0) into (2,5) and transforms (0, 1) to (1,3)? (b) What matrix transforms (2,5) to (1,0) and (1,3) to (0, 1)?

Find the Canonical transformation of the following equation 3 urr +10 Ury +3 Uyy = 0 } 67=y+3x None } } 4: 7=y-3r

The following matrices are given: Matrix A describes the reflection of a point in space on the x, y -plane and matrix B represents the rotation of the spatial coordinate system around the z-axis by the angle alpha (a) Show that both matrices are orthogonal. (b) Find the inverse of the two matrices. (c) Write the following matrices: (i) A matrix that describes the reflection of a point in space on the x, z-plane, (ii) A matrix that describes the rotation of the spatial coordinate system around the y-axis by the angle ß

3) Find the linear transformation that transforms X~N(2,3) to Z~N(0,1). Show that this transformation actually works (find the transformation Z, and show that Hz = 0 and o? = 1).