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Find a matrix for the linear transformation $T : \mathbb R^3 \to \mathbb R^3$ that first rotates a vector by an angle of 30◦ in the counterclockwise direction about the y-axis, then reflects the vector about the xz-plane, and lastly projects the vector onto the yz-plane.
How would you illustrate a matrix transformation reflecting about the xz-plane in an $\mathbb R^3$ space?
Send $y$ to $-y$. The matrix is given by $\begin{pmatrix} 1 & 0 & 0 \\ 0 &-1 &0\\ 0 & 0 &1 \end{pmatrix} $.
