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...
Related questions
Question
100%
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86847a45-621f-4eb2-b143-0cde4fac410f%2Ff883cea2-25f1-4754-96b2-3f97453fdc3a%2Frfdpj44_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning