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Show that the matrix C=(-2) is a linear combination of the matrices A-(-2 5) v 8=6 6) if so, state the value of the scalars.

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Answer to a math question Show that the matrix C=(-2) is a linear combination of the matrices A-(-2 5) v 8=6 6) if so, state the value of the scalars.

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Tiffany
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103 Answers
1. Let's denote the given matrices:
A = \begin{pmatrix}-2 & 5 \\8 & 6\end{pmatrix}, \quad B = \begin{pmatrix}-2\end{pmatrix}, \quad C = \begin{pmatrix}-2\end{pmatrix}

2. We need to find scalars \alpha and \beta such that:
\alpha A + \beta B = C

3. Checking suitable values:
\alpha \begin{pmatrix}-2 & 5 \\8 & 6\end{pmatrix} + \beta \begin{pmatrix}-2\end{pmatrix} = \begin{pmatrix}-2\end{pmatrix}

4. Comparing matrix dimensions and entries, we see that matrix multiplication only affects the element:
0A + 1B = 0 \begin{pmatrix}-2 & 5 \\8 & 6\end{pmatrix} + 1 \begin{pmatrix}-2\end{pmatrix}

5. Thus:
C = 0A + 1B = \begin{pmatrix}-2\end{pmatrix}

Answer:
C = 0A + 1B
with scalars 0 and 1.

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