Let $ V=\mathbb{R}^3$ . Let

$ (i)$ $ T:V \to V$ be rotation by angle $ \theta$ counterclockwise in the plane (through origin) perpendicular to $ \ (1,2,3)$ ,

$ (ii)$ $ \ S : V \to V$ be the reflection with respect to the plane (through origin) spanned by the vectors $ (1,0,1), \ (1,2,1)$ ,

$ (iii)$ $ U: V \to V $ be the rotation by the angle $ \phi$ counterclockwise in the plane ( through origin) perpendicular to $ (1,0,1)$ .

Then find the matrix of $ \ U \circ S \circ T$ with respect to the standard basis.

**Answer:**

To answer the question we have to find the matrices of $ \ T, S, U$ and then combine the matrices.

But I can’t find the matrices.

Help me