Consider the following system of linear equations: Use the Gaussian elimination method to determine all values of k (if any) so that the system: x+y + 4z = 2 2x + 3y +12z =k² -3x+y+ 4z = 4k+2 a) is inconsistent. b) has infinitely many solutions. c) Referring to answer in (b) and k is a positive value, determine the value of x, y, and z. Hence illustrate the system using Geogebra 3D and label the intersection point(s) if any.
Consider the following system of linear equations: Use the Gaussian elimination method to determine all values of k (if any) so that the system: x+y + 4z = 2 2x + 3y +12z =k² -3x+y+ 4z = 4k+2 a) is inconsistent. b) has infinitely many solutions. c) Referring to answer in (b) and k is a positive value, determine the value of x, y, and z. Hence illustrate the system using Geogebra 3D and label the intersection point(s) if any.
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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Consider the following system of linear equations:
Use the Gaussian elimination method to determine all values of k (if any) so that the
system:
x + y + 4z = 2
2x + 3y +12z =k²
-3x+y+ 4z = 4k+2
a) is inconsistent.
b) has infinitely many solutions.
c) Referring to answer in (b) and k is a positive value, determine the value of x, y,
and z. Hence illustrate the system using Geogebra 3D and label the intersection
point(s) if any.
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