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Let a be a real number, and consider the following homogeneous system of linear equations: x + y+ z = 0 ax + 4y + z = 0 6x + (a + 2)y + 2z = 0 For what value(s) of a will the system have non-trivial solutions? If no such a exists, explain why. Otherwise, find the basic solutions to the system and express the general solution as a linear combination of these basic solutions.

Let a be a real number, and consider the following homogeneous system of linear equations: x + y+ z = 0 ax + 4y + z = 0 6x + (a + 2)y + 2z = 0 For what value(s) of a will the system have non-trivial solutions? If no such a exists, explain why. Otherwise, find the basic solutions to the system and express the general solution as a linear combination of these basic solutions.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let a be a real number, and consider the following homogeneous system of linear equations: x + y + z = 0 ax + 4y + z = 0 6x + (a + 2)y + 2z = 0 For what value(s) of a will the system have non-trivial solutions? If no such a exists, explain why. Otherwise, find the basic solutions to the system and express the general solution as a linear combination of these basic solutions.
Transcribed Image Text:Let a be a real number, and consider the following homogeneous system of linear equations: x + y + z = 0 ax + 4y + z = 0 6x + (a + 2)y + 2z = 0 For what value(s) of a will the system have non-trivial solutions? If no such a exists, explain why. Otherwise, find the basic solutions to the system and express the general solution as a linear combination of these basic solutions.
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