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.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.5: Cramer's Rule
Problem 35PS
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