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Let's solve the given numerical problems step by step. ### Given Vectors: \[ \mathbf{a} = \begin{pmatrix}1\\2\\3\end{pmatrix},\quad \mathbf{b} = \begin{pmatrix}-2\\1\\-3\end{pmatrix},\quad \mathbf{c} = \begin{pmatrix}-2\\-1\\1\end{pmatrix} \] #### 1. Compute \( 2\mathbf{a} - 5\mathbf{b} \): \[ 2\mathbf{a} = 2 \times \begin{pmatrix}1\\2\\3\end{pmatrix} = \begin{pmatrix}2\\4\\6\end{pmatrix} \] \[ 5\mathbf{b} = 5 \times \begin{pmatrix}-2\\1\\-3\end{pmatrix} = \begin{pmatrix}-10\\5\\-15\end{pmatrix} \] \[ 2\mathbf{a} - 5\mathbf{b} = \begin{pmatrix}2\\4\\6\end{pmatrix} ____ ___ ____ ______ _________ _______ ____ __________ ________ _______ ____ _______.
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