The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v., v, and v because 0 = Ov, + 0v2 + Ov3. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v., v,, and v. If not possible, enter IMPOSSIBLE.) V1 = (1, 0, 1), V2 = (-1, 1, 2), V3 = (0, 1, 6) 0 =
The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v., v, and v because 0 = Ov, + 0v2 + Ov3. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v., v,, and v. If not possible, enter IMPOSSIBLE.) V1 = (1, 0, 1), V2 = (-1, 1, 2), V3 = (0, 1, 6) 0 =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The zero vector \( \mathbf{0} = (0, 0, 0) \) can be written as a linear combination of the vectors \( \mathbf{v_1}, \mathbf{v_2}, \) and \( \mathbf{v_3} \) because
\[ \mathbf{0} = 0\mathbf{v_1} + 0\mathbf{v_2} + 0\mathbf{v_3}. \]
This is called the trivial solution. Can you find a nontrivial way of writing \( \mathbf{0} \) as a linear combination of the three vectors? (Enter your answer in terms of \( \mathbf{v_1}, \mathbf{v_2}, \) and \( \mathbf{v_3}. \) If not possible, enter IMPOSSIBLE.)
\[
\mathbf{v_1} = (1, 0, 1), \quad \mathbf{v_2} = (-1, 1, 2), \quad \mathbf{v_3} = (0, 1, 6)
\]
\[
\mathbf{0} = \underline{\hspace{2cm}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18936370-e2cc-46bd-a4d0-3c2ee0736afc%2Fb92f618b-8594-467b-ac0d-6fc101e5bf7b%2Fvxhbve_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The zero vector \( \mathbf{0} = (0, 0, 0) \) can be written as a linear combination of the vectors \( \mathbf{v_1}, \mathbf{v_2}, \) and \( \mathbf{v_3} \) because
\[ \mathbf{0} = 0\mathbf{v_1} + 0\mathbf{v_2} + 0\mathbf{v_3}. \]
This is called the trivial solution. Can you find a nontrivial way of writing \( \mathbf{0} \) as a linear combination of the three vectors? (Enter your answer in terms of \( \mathbf{v_1}, \mathbf{v_2}, \) and \( \mathbf{v_3}. \) If not possible, enter IMPOSSIBLE.)
\[
\mathbf{v_1} = (1, 0, 1), \quad \mathbf{v_2} = (-1, 1, 2), \quad \mathbf{v_3} = (0, 1, 6)
\]
\[
\mathbf{0} = \underline{\hspace{2cm}}
\]
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