Problem #4: Suppose you have a consistent system of linear equations, with coefficients in R, which are homogeneous - that is, all the b; are 0. Explain why the set of solutions to this system forms a vector space over R. Then, explain why if the system was not homogeneous (i.e. if at least one of the b¡ is nonz onzero) the set of solutions would definitely NOT form a vector space over R.
Problem #4: Suppose you have a consistent system of linear equations, with coefficients in R, which are homogeneous - that is, all the b; are 0. Explain why the set of solutions to this system forms a vector space over R. Then, explain why if the system was not homogeneous (i.e. if at least one of the b¡ is nonz onzero) the set of solutions would definitely NOT form a vector space over R.
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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![Problem #4: Suppose you[ have a consistent system of linear equations, with coefficients in
R, which are homogeneous - that is, all the b; are 0. Explain why the set of solutions to this
system forms a vector space over R. Then, explain why if the system was not homogeneous
(i.e. if at least one of the b; is nonzero) the set of solutions would definitely NOT form a
vector space over R.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faba5746d-e0e8-46ca-a0bb-ec14000055d1%2Fcf568a53-a6f5-4a9d-9b71-397f98cadf8d%2F5bn7nz_processed.png&w=3840&q=75)
Transcribed Image Text:Problem #4: Suppose you[ have a consistent system of linear equations, with coefficients in
R, which are homogeneous - that is, all the b; are 0. Explain why the set of solutions to this
system forms a vector space over R. Then, explain why if the system was not homogeneous
(i.e. if at least one of the b; is nonzero) the set of solutions would definitely NOT form a
vector space over R.
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