Show that the linear system has at least one solution for any values b1, b2, b3. -4y1 У2 буз + 794 -8y1 + буг Уз +994 6y1 3у3 + 2у4 11y2 = = = 01 b2 b3
Show that the linear system has at least one solution for any values b1, b2, b3. -4y1 У2 буз + 794 -8y1 + буг Уз +994 6y1 3у3 + 2у4 11y2 = = = 01 b2 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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![The problem involves demonstrating that a given linear system has at least one solution for any values \( b_1, b_2, b_3 \).
The linear system is:
\[ -4y_1 - y_2 - 6y_3 + 7y_4 = b_1 \]
\[ -8y_1 + 6y_2 - y_3 + 9y_4 = b_2 \]
\[ 6y_1 - 11y_2 - 3y_3 + 2y_4 = b_3 \]
To solve this, one would typically use techniques such as Gaussian elimination, matrix methods, or examine the properties of the coefficient matrix to ensure it’s nonsingular (i.e., invertible) which guarantees a solution exists for any \( b_1, b_2, b_3 \) due to the invertibility of the matrix formed by the coefficients.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41311914-ae66-4572-a15b-46cf96290e67%2Fc511658b-e959-4bbc-b2d6-d22ec19469aa%2F9lb4h7o_processed.png&w=3840&q=75)
Transcribed Image Text:The problem involves demonstrating that a given linear system has at least one solution for any values \( b_1, b_2, b_3 \).
The linear system is:
\[ -4y_1 - y_2 - 6y_3 + 7y_4 = b_1 \]
\[ -8y_1 + 6y_2 - y_3 + 9y_4 = b_2 \]
\[ 6y_1 - 11y_2 - 3y_3 + 2y_4 = b_3 \]
To solve this, one would typically use techniques such as Gaussian elimination, matrix methods, or examine the properties of the coefficient matrix to ensure it’s nonsingular (i.e., invertible) which guarantees a solution exists for any \( b_1, b_2, b_3 \) due to the invertibility of the matrix formed by the coefficients.
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