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BenBlackburn
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Let V be the span of the vectors (1,3,1,2),(1,2,1,4). Express V as the solution set of a homogenous linear system.
 2 years ago
 2 years ago
BenBlackburn Group Title
Let V be the span of the vectors (1,3,1,2),(1,2,1,4). Express V as the solution set of a homogenous linear system.
 2 years ago
 2 years ago

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colorful Group TitleBest ResponseYou've already chosen the best response.0
I'm not quite sure I understand the question...
 2 years ago

BenBlackburn Group TitleBest ResponseYou've already chosen the best response.0
I was having the same issue. i dont even know where to start lol
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
it's asking to express the general form I suppose?\[A\vec x=\vec0\]and we have\[A=\left[\begin{matrix}1&1\\3&2\\1&1\\2&4\end{matrix}\right]\]and\[\vec x=\left[\begin{array}~x_1\\x_2\\x_3\\x_4\end{array}\right]\]but what does it want us to write exactly?
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
oh that matrix is sideways I think
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
no, it's just that the \(\vec x\) is 2 rows long\[A\vec x=\vec0\]and we have\[A=\left[\begin{matrix}1&1\\3&2\\1&1\\2&4\end{matrix}\right]\]and\[\vec x=\left[\begin{array}~x_1\\x_2\end{array}\right]\]but what does it want us to write?
 2 years ago

BenBlackburn Group TitleBest ResponseYou've already chosen the best response.0
ummm i have no clue
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
well, the solution set is supposed to be the vector space, so we need to write the set of all solution in set notation somehow it seems
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
but it says the "homogeneous solution" so I guess let's first solve the above
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
but I'm thinking maybe homogeneous doesn't mean =0
 2 years ago

BenBlackburn Group TitleBest ResponseYou've already chosen the best response.0
ohhhh ya i think it does mean =0
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
so then I think that the span is the set\[V=\{\vec x:A\vec x=\vec0\}\]where\[A=\left[\begin{matrix}1&1\\3&2\\1&1\\2&4\end{matrix}\right]\]
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
not sure how exactly they want you to state it, but the set of all vectors that solve that system seems to be the vector space they are talking about
 2 years ago

BenBlackburn Group TitleBest ResponseYou've already chosen the best response.0
so its just saying to express the V as the solution set of a homogenious system?
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
usually the span of those vectors is the set of all linear combinations of those vectors, so you if not for the word "homogenous" I would say the span is just\[S=\{c_1\langle1,3,1,2\rangle\},c_2\langle1,2,1,4\rangle\}\]
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
typo, I meant \[S=\{c_1\langle1,3,1,2\rangle,c_2\langle1,2,1,4\rangle\}\]
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
hard to know what they want you to write exactly imo
 2 years ago

BenBlackburn Group TitleBest ResponseYou've already chosen the best response.0
correct i definitely see that
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.0
but I don't think what I just wrote is "homogenous"
 2 years ago
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