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 2 years ago
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
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.

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

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

colorful
 2 years ago
Best ResponseYou've already chosen the best response.0it'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?

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

colorful
 2 years ago
Best ResponseYou've already chosen the best response.0no, 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?

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

colorful
 2 years ago
Best ResponseYou've already chosen the best response.0well, 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

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

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

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

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

colorful
 2 years ago
Best ResponseYou've already chosen the best response.0not 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

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

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

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

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

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

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