#### Answer

The statement “Given two non-zero vectors $\mathbf{v}$ and $\mathbf{w}$, $\mathbf{v}$ can be decomposed into two vectors, one parallel to $\mathbf{w}$ and the other orthogonal to $\mathbf{w}$.” is true.

#### Work Step by Step

The statement is true as a given vector can be decomposed into two vectors, such that one vector is parallel to the given vector and the other is orthogonal to the given vector.