Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
**Exercises 3–6: Finding Coordinate Vectors in Subspace** In Exercises 3–6, the vector \( \mathbf{x} \) is in a subspace \( H \) with a basis \( \mathcal{B} = \{\mathbf{b}_1, \mathbf{b}_2\} \). Find the \( \mathcal{B} \)-coordinate vector of \( \mathbf{x} \). **Exercise 3:** \[ \mathbf{b}_1 = \begin{bmatrix} 1 \\ -4 \end{bmatrix}, \mathbf{b}_2 = \begin{bmatrix} -2 \\ 7 \end{bmatrix}, \mathbf{x} = \begin{bmatrix} -3 \\ 7 \end{bmatrix} \] **Exercise 4:** \[ \mathbf{b}_1 = \begin{bmatrix} 1 \\ -3 \end{bmatrix}, \mathbf{b}_2 = \begin{bmatrix} -3 \\ 5 \end{bmatrix}, \mathbf{x} = \begin{bmatrix} -7 \\ 5 \end{bmatrix} \]
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Transcribed Image Text:**Exercises 3–6: Finding Coordinate Vectors in Subspace** In Exercises 3–6, the vector \( \mathbf{x} \) is in a subspace \( H \) with a basis \( \mathcal{B} = \{\mathbf{b}_1, \mathbf{b}_2\} \). Find the \( \mathcal{B} \)-coordinate vector of \( \mathbf{x} \). **Exercise 3:** \[ \mathbf{b}_1 = \begin{bmatrix} 1 \\ -4 \end{bmatrix}, \mathbf{b}_2 = \begin{bmatrix} -2 \\ 7 \end{bmatrix}, \mathbf{x} = \begin{bmatrix} -3 \\ 7 \end{bmatrix} \] **Exercise 4:** \[ \mathbf{b}_1 = \begin{bmatrix} 1 \\ -3 \end{bmatrix}, \mathbf{b}_2 = \begin{bmatrix} -3 \\ 5 \end{bmatrix}, \mathbf{x} = \begin{bmatrix} -7 \\ 5 \end{bmatrix} \]
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