The problem you're referring to involves finding a linear combination of vectors. Specifically, you are asked to find different scalars $a$, $b$, and $c$ so that the given vector $\begin{bmatrix} 7 \\ 9 \end{bmatrix}$ can be expressed as a linear combination of vectors $v$, $w$, and $r$, which seem to be from an earlier part of the exercise.

Let's break this down step by step:

Task:

• You need to find scalars $a$, $b$, and $c$ such that: $a v + b w + c r = \begin{bmatrix} 7 \\ 9 \end{bmatrix}$ where $v$, $w$, and $r$ are vectors provided elsewhere in the problem.

General Approach:

• Express this linear combination as a system of linear equations by equating the components of the vectors.

  If the vectors are in $\mathbb{R}^2$, you will get two equations: [ a(v_1) + b(w_1) + c