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jcd2012
Group Title
Linear Algebra: Find (if possible) values a, b, and c such that the system of linear equations has:
a) no solution
b) exactly one solution
c) infinitely many solutions
2x  y + z = a
x +y +2z = b
3y + 3z = c
 one year ago
 one year ago
jcd2012 Group Title
Linear Algebra: Find (if possible) values a, b, and c such that the system of linear equations has: a) no solution b) exactly one solution c) infinitely many solutions 2x  y + z = a x +y +2z = b 3y + 3z = c
 one year ago
 one year ago

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jcd2012 Group TitleBest ResponseYou've already chosen the best response.0
dw:1348174076973:dw
 one year ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
Try turning that into eschelon form.
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
I am thinking a bit differently...
 one year ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
Yeah, I skimmed through a textbok about 30 mins ago, I'm haven't exactly even taken this ;). I know a solution though, it's probably not the most efficient way...
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
I'm not sure myself either...
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
For any \(n\times n\) matrix \(A\) the system\[A\vec x=\vec b\]has exactly one solution for each \(n\times1\) matrix \(\vec b\) if and only if \(\det A\neq0\)
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
so what does a,b, and c have to do with the answer to your question I'm not even sure, the answer seems to be dependent on the matrix \(A\)....
 one year ago

jcd2012 Group TitleBest ResponseYou've already chosen the best response.0
a, b, and c are any real number such that each condition is met
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
right, any matrix \(\vec b\)
 one year ago

jcd2012 Group TitleBest ResponseYou've already chosen the best response.0
dw:1348174993843:dw
 one year ago

jcd2012 Group TitleBest ResponseYou've already chosen the best response.0
now, do I look for conditions in which the three cases can be met?
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
if this is always true then there are infinite solutions, so that would suggest that a=3, c=3, and b is whatever (easy to figure out) how to test the other two conditions I'm not so sure
 one year ago

jcd2012 Group TitleBest ResponseYou've already chosen the best response.0
I'll start with that then. these kinds of questions happen to be the even numbered problems. thanks
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
sure, wish I could help more
 one year ago
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