For vectors (x, y, z) € R³ consider the inhomogeneous linear system: x=y+z=3, and its 'associated' homogeneous linear system: x=y+z=0. (a) Express both systems in matrix form Mr = c. (b) Show that (0, 0,3) is a solution of the inhomogeneous system. (c) Show that the set of solutions of the inhomogeneous system is given by S = {(s, t, 3-s+t): s₁t € R} CR³.
For vectors (x, y, z) € R³ consider the inhomogeneous linear system: x=y+z=3, and its 'associated' homogeneous linear system: x=y+z=0. (a) Express both systems in matrix form Mr = c. (b) Show that (0, 0,3) is a solution of the inhomogeneous system. (c) Show that the set of solutions of the inhomogeneous system is given by S = {(s, t, 3-s+t): s₁t € R} CR³.
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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Transcribed Image Text:For vectors (x, y, z) = R³ consider the inhomogeneous linear system:
x=y+z=3,
and its 'associated' homogeneous linear system:
x=y+z=0.
(a) Express both systems in matrix form Mr = c.
(b) Show that (0, 0, 3) is a solution of the inhomogeneous system.
(c) Show that the set of solutions of the inhomogeneous system is given by
S = {(s, t, 3-s+t): s₁t € R} CR³.
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