1. The problem is to determine if the vector $\mathbf{u}$ is a linear combination of the vectors $\mathbf{v_1}$, $\mathbf{v_2}$, and $\mathbf{v_3}$. 2. A vector $\mathbf{u}$ is a linear combination of vectors $\mathbf{v_1}$, $\mathbf{v_2}$, and $\mathbf{v_3}$ if there exist scalars $a$, $b$, and $c$ such that: $$\mathbf{u} = a\mathbf{v_1} + b\mathbf{v_2} + c\mathbf{v_3}$$ 3. Here are example vectors: $$\mathbf{u} = \begin{bmatrix} 3 \\ 5 \\ 7 \end{bmatrix}, \quad \mathbf{v_1} = \begin{bmatrix} 1 \\ 0 \\ 2 \end{bmatrix}, \quad \mathbf{v_2} = \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix}, \quad \mathbf{v_3} = \begin{bmatrix} 2 \\ 1 \\ 3 \end{bmatrix}$$ These vectors can be used to check if $\mathbf{u}$ is a linear combination of $\mathbf{v_1}$, $\mathbf{v_2}$, and $\mathbf{v_3}$.