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Find w such that 2u + v- 3w = 0. W= u= (2, 7, 5, 0), v = (-8, -3, 1, 4) Need Help? Read It

Find w such that 2u + v- 3w = 0. W= u= (2, 7, 5, 0), v = (-8, -3, 1, 4) Need Help? Read It

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem Statement:** Find \( w \) such that \( 2\mathbf{u} + \mathbf{v} - 3\mathbf{w} = 0 \). Given vectors: \[ \mathbf{u} = (2, 7, 5, 0) \] \[ \mathbf{v} = (-8, -3, 1, 4) \] **Solution:** \[ \mathbf{w} = \] **Need Help?** [Read It] (Interactive button for additional help) --- **Explanation:** This problem involves finding a vector \(\mathbf{w}\) such that a linear combination of given vectors \(\mathbf{u}\) and \(\mathbf{v}\), with the vector \(\mathbf{w}\), results in the zero vector. The task is to solve for the unknown vector \(\mathbf{w}\). To find \(\mathbf{w}\), you equate components of the given vectors according to the equation \(2\mathbf{u} + \mathbf{v} - 3\mathbf{w} = 0\) and solve for each component of \(\mathbf{w}\).
Transcribed Image Text:**Problem Statement:** Find \( w \) such that \( 2\mathbf{u} + \mathbf{v} - 3\mathbf{w} = 0 \). Given vectors: \[ \mathbf{u} = (2, 7, 5, 0) \] \[ \mathbf{v} = (-8, -3, 1, 4) \] **Solution:** \[ \mathbf{w} = \] **Need Help?** [Read It] (Interactive button for additional help) --- **Explanation:** This problem involves finding a vector \(\mathbf{w}\) such that a linear combination of given vectors \(\mathbf{u}\) and \(\mathbf{v}\), with the vector \(\mathbf{w}\), results in the zero vector. The task is to solve for the unknown vector \(\mathbf{w}\). To find \(\mathbf{w}\), you equate components of the given vectors according to the equation \(2\mathbf{u} + \mathbf{v} - 3\mathbf{w} = 0\) and solve for each component of \(\mathbf{w}\).
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