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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

Can you find a different set of scalars a, b, and c so that you also get vector [7,9] as a linear combination of vectors v, w, and r?

Discover how to find scalars a, b, and c that express the vector [7,9] as a linear combination of the vectors v, w, and r. Learn key concepts from linear algebra, including the linear combination theorem, vector spaces, and solving systems of linear equations.

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