chrisplusian
  • chrisplusian
A question about linear algebra.... See attachment please
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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chrisplusian
  • chrisplusian
1 Attachment
chrisplusian
  • chrisplusian
My question is...... are there times when you can't express the result as a linear combination of the two others?
chrisplusian
  • chrisplusian
If so is what clues you in on that?

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ganeshie8
  • ganeshie8
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 \((2,0)\) ?
chrisplusian
  • chrisplusian
So when you say the vector (2,2) that would be \[a_{1}=\left(\begin{matrix}2 \\ 2\end{matrix}\right)\] correct?
ganeshie8
  • ganeshie8
right
chrisplusian
  • chrisplusian
ok give me a second to try it out
ganeshie8
  • ganeshie8
take ur time
chrisplusian
  • chrisplusian
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
chrisplusian
  • chrisplusian
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?
ganeshie8
  • ganeshie8
so what do you conclude ?
ganeshie8
  • ganeshie8
Yes, there is a method. Before getting to that, I just want to see you get the idea of taking linear combinations of vectors..
chrisplusian
  • chrisplusian
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
chrisplusian
  • chrisplusian
And I am not sure i am getting the idea your referring to
ganeshie8
  • ganeshie8
I am not referring to any idea yet
ganeshie8
  • ganeshie8
The present problem is cooked up to be done by visual inspection
chrisplusian
  • chrisplusian
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
ganeshie8
  • ganeshie8
for part (i), try \(3a_1 + 2a_2\)
ganeshie8
  • ganeshie8
for part (ii), try \(3a_1 + 4a_2\)
chrisplusian
  • chrisplusian
I actually found a solution for both....
1 Attachment
chrisplusian
  • chrisplusian
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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