#*determine dimension of Nul A* Question 14

81 messages · Page 1 of 1 (latest)

sullen anvil
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So I have been working on linear algebra and I understand how to find Column space but in this case im having so much trouble figuring out how to find Nul A. All the explanations I find are not really hitting me.

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wicked bridgeBOT
sullen anvil
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Am I high or is the answer suppose to be that it has 3 dimensions for Nul because 3 free variables?

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I was wondering if I was going to find the values of those free variables how would I do it?

icy axle
timid dome
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im learning this now too

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i need to do my hw

icy axle
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I already see they are in echelon form.

tiny raft
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dim(A) = rank(A) + nullity(A)

sullen anvil
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@tiny raft that seems helpful. However, rank is in the next chapter section and im not there yet to understanding this

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@icy axle can you show me what you mean? step by step

timid dome
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The rank is equal to the number of pivots in the reduced row echelon form, and is the maximum number of linearly independent columns that can be chosen from the matrix.

sullen anvil
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so that would be 3?

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for the pivots

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i guess my next question is are col 5 and 6 independent or not? I know 2 isnt.

timid dome
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yeah

timid dome
sullen anvil
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so i have my pivots (rank) and youre saying my number of linear independent columns is 5,

icy axle
sullen anvil
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one sec

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Would i just pick random numbers for x2,x5,x6?

icy axle
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yes

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no not random numbers

sullen anvil
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if i throw 0's in i guess that would give me a solution

icy axle
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they are free

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you have infinite many solutions

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it's just

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x2, x5 and x6 can by anything

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basically NulA is the vector space that is span by those 3 vectors

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If you write it like:

x2[...] + x5[...] + x6[...]

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it's basically the span

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all linear combinations since x2, x5 and x6 are in R

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so dimension would be also 3

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of Nul A

sullen anvil
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let me right this out

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in this example i was confused by the values they put into the vectors next to x2 and x4

icy axle
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what values?

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I read "free variables"

sullen anvil
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{-2,1,0,0,0}

icy axle
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oh no

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that just because they factored x2 and x4

icy axle
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x5 = 0 due to the system

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-7x_5 = 0 -> x_5 = 0

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also since x2 and x4 are the free variables we make every component in terms of these variables

untold walrusBOT
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𝔸dωn𝓲²s

587715738484211754.png
icy axle
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Notice these are the coefficients

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fine I'll write it out

untold walrusBOT
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𝔸dωn𝓲²s

587715738484211754.png
sullen anvil
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that is spicy

icy axle
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that's what they did

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and what i did

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for educational purposes

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Left

untold walrusBOT
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𝔸dωn𝓲²s

587715738484211754.png
icy axle
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And that's how the game works everytime, when doing these.

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You solve some system and figure the dimension by counting the free variables

sullen anvil
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alright if im ever asked for the basis, I will know what to do. I will proatice this tomorrow morning.

icy axle
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dedication

sullen anvil
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how do i say this post is finish?

icy axle
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type: finsih

sullen anvil
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finish

icy axle
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no

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finsih

sullen anvil
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finsih

icy axle
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.solved

wicked bridgeBOT
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Solved

Post marked as solved by @icy axle.

Use .unsolved if this was a mistake.

sullen anvil
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.solved

icy axle
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.unsolved

wicked bridgeBOT
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Unsolved

Post marked as unsolved by @icy axle.

Use .solved to mark as solved.

icy axle
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now do it lmao

sullen anvil
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ok boss

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.solved

wicked bridgeBOT
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Solved

Post marked as solved by @sullen anvil.

Use .unsolved if this was a mistake.

icy axle
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😂

sullen anvil
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lol

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@icy axle is it possible to ask you able terminology?

icy axle
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sure!