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

Calculus: Early Transcendentals

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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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.

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