2v1 +3V2 + V3 V4 +5V5 (V3 and V4 are multiplied) is a linear combination of the vectors V1, V2, V3, V4, V5. True False
2v1 +3V2 + V3 V4 +5V5 (V3 and V4 are multiplied) is a linear combination of the vectors V1, V2, V3, V4, V5. True False
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb04829d0-4645-426e-bf1a-7ada40b0786f%2Fe925bf3c-a391-4109-8c64-b15370ff4205%2Fc57237_processed.jpeg&w=3840&q=75)
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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