5.Please show work step by step with clear written **Problem: Express the Indicated Vector as a Linear Combination****Objective:**Express the vector \( w \) as a linear combination of the given vectors \( u \) and \( v \), if possible.**Vectors Given:**- \( w = (1, 0, -7) \)- \( u = (5, 3, 4) \)- \( v = (3, 2, 5) \)**Analysis:**To express \( w \) as a linear combination of \( u \) and \( v \), we look for scalars \( a \) and \( b \) such that:\[ w = a \cdot u + b \cdot v \]This translates to solving the system of equations:\[ a \cdot (5, 3, 4) + b \cdot (3, 2, 5) = (1, 0, -7) \]Which yields:1. \( 5a + 3b = 1 \)2. \( 3a + 2b = 0 \)3. \( 4a + 5b = -7 \)**Solution Approach:**To find \( a \) and \( b \), solve the above system of linear equations. Determine if a solution exists and solve for the values of \( a \) and \( b \) if possible.

Given that, W = ( 1, 0 , -7) u = ( 5, 3 , 4) V = ( 3, 2, 5) Let the a and b be the any scalar…

Answered: Express the indicated vector w as a…

Express the indicated vector w as a linear combination of the given vectors u,v if possible. w = (1,0,–7), u = (5,3,4), v= (3,2,5) %3D

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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