anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I'm not quite sure I understand the question...
anonymous
  • anonymous
I was having the same issue. i dont even know where to start lol
anonymous
  • anonymous
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?

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anonymous
  • anonymous
oh that matrix is sideways I think
anonymous
  • anonymous
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?
anonymous
  • anonymous
ummm i have no clue
anonymous
  • anonymous
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
anonymous
  • anonymous
but it says the "homogeneous solution" so I guess let's first solve the above
anonymous
  • anonymous
but I'm thinking maybe homogeneous doesn't mean =0
anonymous
  • anonymous
ohhhh ya i think it does mean =0
anonymous
  • anonymous
so then I think that the span is the set\[V=\{\vec x:A\vec x=\vec0\}\]where\[A=\left[\begin{matrix}1&-1\\3&2\\-1&-1\\2&-4\end{matrix}\right]\]
anonymous
  • anonymous
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
anonymous
  • anonymous
so its just saying to express the V as the solution set of a homogenious system?
anonymous
  • anonymous
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\[S=\{c_1\langle1,3,-1,2\rangle\},c_2\langle-1,2,-1,4\rangle\}\]
anonymous
  • anonymous
typo, I meant \[S=\{c_1\langle1,3,-1,2\rangle,c_2\langle-1,2,-1,4\rangle\}\]
anonymous
  • anonymous
hard to know what they want you to write exactly imo
anonymous
  • anonymous
correct i definitely see that
anonymous
  • anonymous
but I don't think what I just wrote is "homogenous"

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