4. Consider a nonhomogeneous system (I): Ar = b and the associated homogeneous system (II):Ar = 0. Which of the following statements is not true. (a) Any linear combination of two solutions of (I) is a solution of (I). (b) Any linear combination of two solutions of (II) is a solution of (II). (c) The difference of two solutions of (I) is a solution of (II). (d) Every solution of (I) is a sum of a solution of (II) and a solution of (I).

4. Consider a nonhomogeneous system (I): Ar = b and the associated homogeneous system (II):Ar = 0. Which of the following statements is not true. (a) Any linear combination of two solutions of (I) is a solution of (I). (b) Any linear combination of two solutions of (II) is a solution of (II). (c) The difference of two solutions of (I) is a solution of (II). (d) Every solution of (I) is a sum of a solution of (II) and a solution of (I).

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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4. Consider a nonhomogeneous system (I): Ar = b and the associated homogeneous system
(II):Ar = 0. Which of the following statements is not true.
(a) Any linear combination of two solutions of (I) is a solution of (I).
(b) Any linear combination of two solutions of (II) is a solution of (II).
(c) The difference of two solutions of (I) is a solution of (II).
(d) Every solution of (I) is a sum of a solution of (II) and a solution of (I).

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