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Mark the following either true or false. Justification is required. . The homogeneous equation Ax = 0 has a nontrivial solution if and only if the corresponding linear system has at least one free variables. If the zero vector is a solution of the equation Az = b, then the system is homogeneous. The solution set of Ar= b can be obtained by translating the solution set of the homogeneous equation Ar = 0. solutions to linear systems (or equivalent matrix or vector equations) should be written in para- metric vector form.

Mark the following either true or false. Justification is required. . The homogeneous equation Ax = 0 has a nontrivial solution if and only if the corresponding linear system has at least one free variables. If the zero vector is a solution of the equation Az = b, then the system is homogeneous. The solution set of Ar= b can be obtained by translating the solution set of the homogeneous equation Ar = 0. solutions to linear systems (or equivalent matrix or vector equations) should be written in para- metric vector form.

Advanced Engineering Mathematics
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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Mark the following either true or false. Justification is required. The homogeneous equation Ax = 0 has a nontrivial solution if and only if the corresponding linear system has at least one free variables. If the zero vector is a solution of the equation Ar = b, then the system is homogeneous. The solution set of Ar = b can be obtained by translating the solution set of the homogeneous equation Ax = 0. solutions to linear systems (or equivalent matrix or vector equations) should be written in para- metric vector form.
Transcribed Image Text:Mark the following either true or false. Justification is required. The homogeneous equation Ax = 0 has a nontrivial solution if and only if the corresponding linear system has at least one free variables. If the zero vector is a solution of the equation Ar = b, then the system is homogeneous. The solution set of Ar = b can be obtained by translating the solution set of the homogeneous equation Ax = 0. solutions to linear systems (or equivalent matrix or vector equations) should be written in para- metric vector form.
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