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 2 years ago
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
 2 years ago
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

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inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Try turning that into eschelon form.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1I am thinking a bit differently...

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah, 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...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1I'm not sure myself either...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1For 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 \(\det A\neq0\)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1so 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 \(A\)....

jcd2012
 2 years ago
Best ResponseYou've already chosen the best response.0a, b, and c are any real number such that each condition is met

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1right, any matrix \(\vec b\)

jcd2012
 2 years ago
Best ResponseYou've already chosen the best response.0now, do I look for conditions in which the three cases can be met?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1if 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

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

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1sure, wish I could help more
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