Linear dependence | Mathematics | Page 1

jade shard Oct 12, 2025, 12:32 PM

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For part a, do they mean that we should form 3 scalar equations and to see if the variables that we find work for all 3 equations?

lunar portal Oct 12, 2025, 12:41 PM

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jade shard For part a, do they mean that we should form 3 scalar equations and to see if th...

It's basically means if (3,7,2) can be expressed as a linear combination of the other three that is
(3,7,2)=a.T_1 + b.v_2 + c.v_3

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Now do you know how to do that

jade shard Oct 12, 2025, 12:47 PM

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lunar portal Now do you know how to do that

yep do I need to use crammer's rule/row-reducing form or can I just substitute?

lunar portal Oct 12, 2025, 12:47 PM

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Substitute what?

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Method of substitution you mean?

jade shard Oct 12, 2025, 12:48 PM

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yes

lunar portal Oct 12, 2025, 12:48 PM

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Well first of all you need to know if a solution exists

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Anyways there are many ways, I'd just do row reduction

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If you want to calculate determinants and inverses you're free to do so as well

jade shard Oct 12, 2025, 12:49 PM

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okay I'll try it out

lunar portal Oct 12, 2025, 12:49 PM

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Sure lmk

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If you need help with anything else

jade shard Oct 12, 2025, 12:50 PM

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appreciate it

jade shard Oct 12, 2025, 1:20 PM

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lunar portal Anyways there are many ways, I'd just do row reduction

Is this approach correct?

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Except now that I can't find any of the variables since the last row reduces to 0

lunar portal Oct 12, 2025, 1:21 PM

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Yes that means it has no solutions

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So the answer to a is no you can write v_4 as a linear combination of the other 3

jade shard Oct 12, 2025, 1:23 PM

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lunar portal So the answer to a is no you can write v_4 as a linear combination of the other ...

Do you mean av1+bv2+cv3=v4?

lunar portal Oct 12, 2025, 1:24 PM

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Yeah there is no such a,b,c

lunar portal Oct 12, 2025, 1:24 PM

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jade shard Do you mean av1+bv2+cv3=v4?

So that this happens

jade shard Oct 12, 2025, 1:24 PM

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Oh okayss got it tyy

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so part b is just no answer?

lunar portal Oct 12, 2025, 1:25 PM

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T_4 lies outside the linear span of the other 3

jade shard Oct 12, 2025, 1:26 PM

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lunar portal T_4 lies outside the linear span of the other 3

Oh that's it?

lunar portal Oct 12, 2025, 1:26 PM

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I think so. If we did all the calculations correctly

jade shard Oct 12, 2025, 1:27 PM

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Damn

jade shard Oct 12, 2025, 1:27 PM

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lunar portal I think so. If we did all the calculations correctly

And part c is the same method as part a except that our v4 changes right?

lunar portal Oct 12, 2025, 1:28 PM

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Yes

jade shard Oct 12, 2025, 1:28 PM

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Alr I'll work it out rq

lunar portal Oct 12, 2025, 1:28 PM

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I'd advise you to still check your calculations

jade shard Oct 12, 2025, 1:53 PM

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lunar portal I'd advise you to still check your calculations

Hmm same as before no solutions

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For part c

jade shard Oct 12, 2025, 6:48 PM

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is that all I need to show?

lunar portal Oct 12, 2025, 7:01 PM

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I think so, but I'm not checking your calculations

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Do you want me to check them?

jade shard Oct 12, 2025, 7:03 PM

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lunar portal Do you want me to check them?

yes :p

lunar portal Oct 12, 2025, 7:03 PM

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Alright

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Yeah looks correct to me

jade shard Oct 12, 2025, 7:09 PM

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lunar portal Yeah looks correct to me

alright thank you for your help!

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+close

bitter otterBOT Oct 12, 2025, 7:09 PM

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jade shard +close

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bitter otterBOT Oct 12, 2025, 7:10 PM

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bitter otter

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#Linear dependence