Show that the linear system has at least one solution for any values b1, b2, b: -4y1 Y2 буз + 794 01 -8y1 + буг уз +994 b2 бу1 1192 3у3 + 274 = b3 = =
Show that the linear system has at least one solution for any values b1, b2, b: -4y1 Y2 буз + 794 01 -8y1 + буг уз +994 b2 бу1 1192 3у3 + 274 = b3 = =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Linear System of Equations
**Problem Statement:**
Show that the linear system has at least one solution for any values \( b_1, b_2, b_3 \).
**System of Equations:**
\[ -4y_1 - y_2 - 6y_3 + 7y_4 = b_1 \]
\[ -8y_1 + 6y_2 - y_3 + 9y_4 = b_2 \]
\[ 6y_1 - 11y_2 - 3y_3 + 2y_4 = b_3 \]
This system of linear equations consists of three equations with four variables \( y_1, y_2, y_3, \) and \( y_4 \). The goal is to demonstrate that there exists at least one solution for every possible set of values for \( b_1, b_2, \) and \( b_3 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41311914-ae66-4572-a15b-46cf96290e67%2Fc6bab6f3-1eeb-4ce3-85fa-36065568a9b8%2Fre1kzna_processed.png&w=3840&q=75)
Transcribed Image Text:### Linear System of Equations
**Problem Statement:**
Show that the linear system has at least one solution for any values \( b_1, b_2, b_3 \).
**System of Equations:**
\[ -4y_1 - y_2 - 6y_3 + 7y_4 = b_1 \]
\[ -8y_1 + 6y_2 - y_3 + 9y_4 = b_2 \]
\[ 6y_1 - 11y_2 - 3y_3 + 2y_4 = b_3 \]
This system of linear equations consists of three equations with four variables \( y_1, y_2, y_3, \) and \( y_4 \). The goal is to demonstrate that there exists at least one solution for every possible set of values for \( b_1, b_2, \) and \( b_3 \).
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