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

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.

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