Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
### Linear Combination Question **Statement:** \[ 2\mathbf{v}_1 + 3\mathbf{v}_2 + \sqrt{3}\mathbf{v}_4 + 5\mathbf{v}_5 \,(\mathbf{v}_3 \text{ and } \mathbf{v}_4 \text{ are multiplied}) \text{ is a linear combination of the vectors } \mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3, \mathbf{v}_4, \mathbf{v}_5. \] **Options:** - ○ True - ○ False **Explanation:** This problem asks whether the given expression can be represented as a linear combination of the specified vectors. In linear algebra, a linear combination involves adding together scalar multiples of vectors. The vectors \(\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3, \mathbf{v}_4, \mathbf{v}_5\) are scalars multiplied by coefficients, suggesting that the expression indeed forms a linear combination using these vectors. The statement includes \( \mathbf{v}_3 \) and \( \mathbf{v}_4 \) being multiplied, indicating potential clarification needs.
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Transcribed Image Text:### Linear Combination Question **Statement:** \[ 2\mathbf{v}_1 + 3\mathbf{v}_2 + \sqrt{3}\mathbf{v}_4 + 5\mathbf{v}_5 \,(\mathbf{v}_3 \text{ and } \mathbf{v}_4 \text{ are multiplied}) \text{ is a linear combination of the vectors } \mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3, \mathbf{v}_4, \mathbf{v}_5. \] **Options:** - ○ True - ○ False **Explanation:** This problem asks whether the given expression can be represented as a linear combination of the specified vectors. In linear algebra, a linear combination involves adding together scalar multiples of vectors. The vectors \(\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3, \mathbf{v}_4, \mathbf{v}_5\) are scalars multiplied by coefficients, suggesting that the expression indeed forms a linear combination using these vectors. The statement includes \( \mathbf{v}_3 \) and \( \mathbf{v}_4 \) being multiplied, indicating potential clarification needs.
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