**Problem 5****Objective:** Determine the linear dependence of the given sets of vectors. If they are linear dependent, find a linear relation.**Vectors:**(a) - $ \mathbf{v}_1 = (2, 1, 0) $- $ \mathbf{v}_2 = (0, 1, 0) $ - $ \mathbf{v}_3 = (-1, 2, 0) $(b)- $ \mathbf{w}_1 = (1, 2, -2) $- $ \mathbf{w}_2 = (3, 1, 0) $- $ \mathbf{w}_3 = (2, -1, 1) $- $ \mathbf{w}_4 = (4, 3, -2) $ **Instructions:**- To determine linear dependence, check if one vector can be expressed as a linear combination of others.- For linear dependence, find coefficients $c_1, c_2, \ldots$ such that $c_1\mathbf{v}_1 + c_2\mathbf{v}_2 + c_3\mathbf{v}_3 = \mathbf{0}$ for set (a), and similarly for set (b).

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Answered: ent, find a linear relation. a) vi =…

ent, find a linear relation. a) vi = (2, 1, 0), V2 = (0, 1,0), V3 = (-1,2,0) %3D b) wi = (1,2, –2), W2 = (3, 1, 0), W3 = (2, –1, 1), W4 = (4, 3, –2)

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

**Problem 5**

**Objective:** Determine the linear dependence of the given sets of vectors. If they are linear dependent, find a linear relation.

**Vectors:**

(a)
- $ \mathbf{v}_1 = (2, 1, 0) $
- $ \mathbf{v}_2 = (0, 1, 0) $
- $ \mathbf{v}_3 = (-1, 2, 0) $

(b)
- $ \mathbf{w}_1 = (1, 2, -2) $
- $ \mathbf{w}_2 = (3, 1, 0) $
- $ \mathbf{w}_3 = (2, -1, 1) $
- $ \mathbf{w}_4 = (4, 3, -2) $

**Instructions:**
- To determine linear dependence, check if one vector can be expressed as a linear combination of others.
- For linear dependence, find coefficients $c_1, c_2, \ldots$ such that $c_1\mathbf{v}_1 + c_2\mathbf{v}_2 + c_3\mathbf{v}_3 = \mathbf{0}$ for set (a), and similarly for set (b).

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