Question 1.8: Find the standard matrix for the linear operator T : R³ → R³......

The linear operator T can be expressed as the composition T\;=\;T_{3}\circ T_{2}\circ T_{1}, where T_{1} is the reflection about the yz-plane,T_{2} is the rotation about z-axis, and T_{3} is the orthogonal projection on the xy-plane. The standard matrices for these linear transformations are T_{1}=\left[{\begin{array}{c c c}{-1}&{0}&{0}\\ {0}&{1}&{0}\\ {0}&{0}&{1}\end{array}}\right] , T_{2}=\left[\begin{array}{c c c}{{\cos\theta}}&{{-\sin\theta}}&{{0}}\\ {{\sin\theta}}&{{\cos\theta}}&{{0}}\\ {{0}}&{{0}}&{{1}}\end{array}\right]at θ = 90°, T_{2}={\left[\begin{array}{c c c}{0}&{-1}&{0}\\ {1}&{0}&{0}\\ {0}&{0}&{1}\end{array}\right]}, and T_{3}={\left[\begin{array}{c c c}{1}&{0}&{0}\\ {0}&{1}&{0}\\ {0}&{0}&{0}\end{array}\right]}.

Therefore, T\;=\;T_{3}\circ T_{2}\circ T_{1}