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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.

  • one year ago
  • one year ago

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  1. colorful Group Title
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    I'm not quite sure I understand the question...

    • one year ago
  2. BenBlackburn Group Title
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    I was having the same issue. i dont even know where to start lol

    • one year ago
  3. colorful Group Title
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    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?

    • one year ago
  4. colorful Group Title
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    oh that matrix is sideways I think

    • one year ago
  5. colorful Group Title
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    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?

    • one year ago
  6. BenBlackburn Group Title
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    ummm i have no clue

    • one year ago
  7. colorful Group Title
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    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

    • one year ago
  8. colorful Group Title
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    but it says the "homogeneous solution" so I guess let's first solve the above

    • one year ago
  9. colorful Group Title
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    but I'm thinking maybe homogeneous doesn't mean =0

    • one year ago
  10. BenBlackburn Group Title
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    ohhhh ya i think it does mean =0

    • one year ago
  11. colorful Group Title
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    so then I think that the span is the set\[V=\{\vec x:A\vec x=\vec0\}\]where\[A=\left[\begin{matrix}1&-1\\3&2\\-1&-1\\2&-4\end{matrix}\right]\]

    • one year ago
  12. colorful Group Title
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    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

    • one year ago
  13. BenBlackburn Group Title
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    so its just saying to express the V as the solution set of a homogenious system?

    • one year ago
  14. colorful Group Title
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    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\[S=\{c_1\langle1,3,-1,2\rangle\},c_2\langle-1,2,-1,4\rangle\}\]

    • one year ago
  15. colorful Group Title
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    typo, I meant \[S=\{c_1\langle1,3,-1,2\rangle,c_2\langle-1,2,-1,4\rangle\}\]

    • one year ago
  16. colorful Group Title
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    hard to know what they want you to write exactly imo

    • one year ago
  17. BenBlackburn Group Title
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    correct i definitely see that

    • one year ago
  18. colorful Group Title
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    but I don't think what I just wrote is "homogenous"

    • one year ago
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