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chrisplusian

  • one year ago

A question about linear algebra.... See attachment please

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  1. chrisplusian
    • one year ago
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  2. chrisplusian
    • one year ago
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    My question is...... are there times when you can't express the result as a linear combination of the two others?

  3. chrisplusian
    • one year ago
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    If so is what clues you in on that?

  4. ganeshie8
    • one year ago
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    Maybe lets try an example in \(xy\) plane first : can you express the vector \((2,2)\) using a linear combination of vectors \((1,0)\) and \((2,0)\) ?

  5. chrisplusian
    • one year ago
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    So when you say the vector (2,2) that would be \[a_{1}=\left(\begin{matrix}2 \\ 2\end{matrix}\right)\] correct?

  6. ganeshie8
    • one year ago
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    right

  7. chrisplusian
    • one year ago
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    ok give me a second to try it out

  8. ganeshie8
    • one year ago
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    take ur time

  9. chrisplusian
    • one year ago
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    I can see it now because both of the "Y" elements are zero then there is no multiple of zero that could combine to equal 2

  10. chrisplusian
    • one year ago
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    Thank you, is there a method in general (by inspection) that I can use to check one of these before attempting to work the problem out?

  11. ganeshie8
    • one year ago
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    so what do you conclude ?

  12. ganeshie8
    • one year ago
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    Yes, there is a method. Before getting to that, I just want to see you get the idea of taking linear combinations of vectors..

  13. chrisplusian
    • one year ago
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    If all X,Y,Z, or Nth element of each vector is zero and the resultant vector is non-zero I can concluded that there is no linear combination of the vectors that will give the correct resultant vector

  14. chrisplusian
    • one year ago
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    And I am not sure i am getting the idea your referring to

  15. ganeshie8
    • one year ago
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    I am not referring to any idea yet

  16. ganeshie8
    • one year ago
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    The present problem is cooked up to be done by visual inspection

  17. chrisplusian
    • one year ago
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    What I meant is you said " I just want to see you get the idea of taking linear combinations of vectors." and honestly I am not sure that I am

  18. ganeshie8
    • one year ago
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    for part (i), try \(3a_1 + 2a_2\)

  19. ganeshie8
    • one year ago
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    for part (ii), try \(3a_1 + 4a_2\)

  20. chrisplusian
    • one year ago
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    I actually found a solution for both....

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  21. chrisplusian
    • one year ago
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    So I was trying to figure out 1) if there was a time this wouldn't work. (which you have shown me) and a way to inspect them and get a definite "NO" sometimes.... if what I am saying makes sense

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