The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂ because 0 Ov₁ + 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 V₁, V₂, and v3. If not possible, enter IMPOSSIBLE.) V₁ = (1, 0, 1), V₂ = (-1, 1, 2), V3 = (0, 3, 6). 0 Need Help? Read It

The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂ because 0 Ov₁ + 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 V₁, V₂, and v3. If not possible, enter IMPOSSIBLE.) V₁ = (1, 0, 1), V₂ = (-1, 1, 2), V3 = (0, 3, 6). 0 Need Help? Read It

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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Question

The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and V3 because 0 = 0v₁ + 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 V₁, V₂, and v3. If not possible, enter IMPOSSIBLE.)
V₁= (1, 0, 1), V₂ = (-1, 1, 2), V3 = (0, 3, 6)
0 =
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Expert Solution

Step 1

Linear Combination:

A vector $V$ is called a linear combination of vectors

$v_{1}, v_{2}, . . ., v_{n}$ if $V$ can be expressed as:

$V = c_{1} v_{1} + c_{2} v_{2} + . . . + c_{n} v_{n}$ ,

where $c_{1}, c_{2}, . . ., c_{n}$ are scalar.

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