Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Let \(\mathbf{v} = \begin{bmatrix} -13 \\ -4 \end{bmatrix}\); \(\mathcal{B} = \left\{ \begin{bmatrix} 4 \\ -4 \end{bmatrix}, \begin{bmatrix} -1 \\ -1 \end{bmatrix} \right\}\); \(\mathcal{C} = \left\{ \begin{bmatrix} -1 \\ 3 \end{bmatrix}, \begin{bmatrix} 1 \\ 1 \end{bmatrix} \right\}\). Find a. \([\mathbf{v}]_{\mathcal{B}}:\) [Answer] b. \([\mathbf{v}]_{\mathcal{C}}:\) [Answer] c. \([\mathcal{B}]_{\mathcal{C}}:\) [Answer] d. \([\mathcal{B}]_{\mathcal{C}}[\mathbf{v}]_{\mathcal{B}}:\) [Answer] e. Are \([\mathcal{B}]_{\mathcal{C}}[\mathbf{v}]_{\mathcal{B}}\) and \([\mathbf{v}]_{\mathcal{C}}\) equal? [Answer]
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Transcribed Image Text:Let \(\mathbf{v} = \begin{bmatrix} -13 \\ -4 \end{bmatrix}\); \(\mathcal{B} = \left\{ \begin{bmatrix} 4 \\ -4 \end{bmatrix}, \begin{bmatrix} -1 \\ -1 \end{bmatrix} \right\}\); \(\mathcal{C} = \left\{ \begin{bmatrix} -1 \\ 3 \end{bmatrix}, \begin{bmatrix} 1 \\ 1 \end{bmatrix} \right\}\). Find a. \([\mathbf{v}]_{\mathcal{B}}:\) [Answer] b. \([\mathbf{v}]_{\mathcal{C}}:\) [Answer] c. \([\mathcal{B}]_{\mathcal{C}}:\) [Answer] d. \([\mathcal{B}]_{\mathcal{C}}[\mathbf{v}]_{\mathcal{B}}:\) [Answer] e. Are \([\mathcal{B}]_{\mathcal{C}}[\mathbf{v}]_{\mathcal{B}}\) and \([\mathbf{v}]_{\mathcal{C}}\) equal? [Answer]
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Step 1: We give definition of coordinate vector.
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Step 2: We solve part (a).
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Step 3: We solve part (b).
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Step 4: We solve part (c).
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Step 5: We solve (d) and (e).
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