For what value(s) of k, if any, will the system have no solution, a unique solution, and infinitely many solutions? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X - 2y + 6z - 2 x + y + z = k 2x - y + 7z = k2 (a) no solution -2,1 (b) unique solution k = DNE (c) infinitely many solutions k -2,3

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.2: Guassian Eliminationa And Guass-jordan Elimination
Problem 54E
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For what value(s) of k, if any, will the system have no solution, a unique solution, and infinitely many solutions? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
X - 2y + 6z - 2
x + y + z = k
2x - y + 7z = k?
(a) no solution
-2,1
(b) unique solution
k = DNE
(c) infinitely many solutions
k
-2,3
Transcribed Image Text:For what value(s) of k, if any, will the system have no solution, a unique solution, and infinitely many solutions? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X - 2y + 6z - 2 x + y + z = k 2x - y + 7z = k? (a) no solution -2,1 (b) unique solution k = DNE (c) infinitely many solutions k -2,3
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