Can you please do this the matrix way because I am desperate please this has to be done using the matrix way and can you do it step by step ---## Orthogonal Vector Problem### Problem Statement1. **Find a vector that is orthogonal to each of the three vectors below:**\[ v_1 = \begin{bmatrix} 1 \\ 1 \\ 4 \\ -1 \end{bmatrix}, \quad v_2 = \begin{bmatrix} 1 \\ 0 \\ 1 \\ 0 \end{bmatrix}, \quad \text{and} \quad v_3 = \begin{bmatrix} -1 \\ 1 \\ 3 \\ 3 \end{bmatrix}. \]### ExplanationTo solve this problem, you need to find a vector $ \mathbf{u} $ such that it is perpendicular (orthogonal) to all given vectors $ \mathbf{v_1} $, $ \mathbf{v_2} $, and $ \mathbf{v_3} $. This means that the dot product of $ \mathbf{u} $ with each of these vectors should equal zero.---This content will help students understand the concept of orthogonality in the context of vectors and how to apply mathematical principles to find a common orthogonal vector in multiple dimensions.

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Find a vector that is orthogonal to each of the three vectors below: V1 = " V2 = 0 and V3 = 1 3 3

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter7: Triangles

Section: Chapter Questions

Problem 1RP: We mentioned in Section 7.5 that our algebraic treatment of vectors could be attributed, in part, to...

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Question

Can you please do this the matrix way because I am desperate please this has to be done using the matrix way and can you do it step by step

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## Orthogonal Vector Problem

### Problem Statement
1. **Find a vector that is orthogonal to each of the three vectors below:**

\[ v_1 = \begin{bmatrix} 1 \\ 1 \\ 4 \\ -1 \end{bmatrix}, \quad v_2 = \begin{bmatrix} 1 \\ 0 \\ 1 \\ 0 \end{bmatrix}, \quad \text{and} \quad v_3 = \begin{bmatrix} -1 \\ 1 \\ 3 \\ 3 \end{bmatrix}. \]

### Explanation
To solve this problem, you need to find a vector $ \mathbf{u} $ such that it is perpendicular (orthogonal) to all given vectors $ \mathbf{v_1} $, $ \mathbf{v_2} $, and $ \mathbf{v_3} $. This means that the dot product of $ \mathbf{u} $ with each of these vectors should equal zero.

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This content will help students understand the concept of orthogonality in the context of vectors and how to apply mathematical principles to find a common orthogonal vector in multiple dimensions.

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