#need help with this

134 messages · Page 1 of 1 (latest)

ember havenBOT
young spindle
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yeah ?

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have you tried anything yet

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@old pasture

old pasture
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i wanna learn how to do it

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can u show solution so i learn from it

young spindle
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let's try a little bit before I give you a solution right away

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cause if I give you a solution and you're confused by it, it's useless

old pasture
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help me to try

young spindle
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so it's better to clear what doubts you have first

old pasture
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so i understand that they want to know if b = 1 and c = 0 is the points of this vector that have M2x2

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right?

young spindle
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I don't get what you're trying to say here

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but you have some set of matrices

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those which have b=1 and c=0

old pasture
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how to find a and d

young spindle
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so for example [[0 1] [0 1]], [[42 1] [0 pi]] are inside this set

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you don't find them

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a and d can be whatever (real number) you want

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there's no constraint on a and d

old pasture
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what do they want me to do in this question

young spindle
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show that this set is a vector space or not

old pasture
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how to do that

young spindle
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i.e. does it satisfy all the vector space axioms or not

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you got a list of these axioms in your notes or not ?

old pasture
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no

young spindle
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aight

old pasture
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what are these

young spindle
old pasture
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what are u v and w

young spindle
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objects in V

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in your question V is the set { [[a b] [c d]] in M2x2 | b=1, c=0}

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and + and . are the usual matrix addition and multiplication

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and you want to see if all these 10 properties are satisfied by V or not

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that's what the question asks

old pasture
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is v abbreviation for vector?

young spindle
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it's a common name you give to a vector yes

old pasture
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okok

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what these 10 propeties

young spindle
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well essentially these encompass all the rules you know with geometric vectors

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you can add them and you can scale them

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and these additions and scaling satisfy certain rules

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the idea behind these axioms is to have a way to talk about objects that behave like geometric vectors

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(but that are not necessarily geometric vectors themselves)

old pasture
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ok what about these

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i have to find the vector of these 4 points

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between each other

young spindle
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aight

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you know determinants?

young spindle
old pasture
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so i imagine a cube

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right

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AB BC CD

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and multipy them by each other

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for AB i do

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x1 - x2 or x2 - x1

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2-3 0 - ( -1 ) 2 - 0

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<-1 , 1 , 2 >

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is AB

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is that right

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@young spindle

young spindle
young spindle
old pasture
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AD?

young spindle
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I'd imagine it's more like a diagonal of the cube or something

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try to pick three vectors which converge at the same point

old pasture
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AB AC AD

young spindle
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you're sure to really have 3 sides like that

old pasture
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ye

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ok now how to find lenght

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from 3 points

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ik from 2

young spindle
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you do as you said

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compute these 3 vectors

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compute the length for each of these 3 vectors

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and multiply the result

old pasture
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was i doing right

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<-1 , 1 , 2 >

young spindle
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well AB would be the opposite of that <1 -1 2>

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but just for computing the length you don't care if you take AB or BA

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they both have the same length

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and that's all we care about here

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length

old pasture
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yea

old pasture
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do i take 2 of them

young spindle
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no

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sqrt((-1)^2 + 1^2 + 2^2)

old pasture
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oh

young spindle
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it's just like the formula for 2D but you add the extra coordinate squared

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for 4D, 5D, 547167516D it works all the same

old pasture
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so its like if it was <1,2>

young spindle
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yea

old pasture
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ok

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that easier than i thought

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and what about second

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first*

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angles

young spindle
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ah yeah we'd need the angles cause we don't have a cube here

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that starts being a pain in the ass

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using determinants is way easier here

old pasture
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sin cos all that

young spindle
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you have a lot of questions :/

old pasture
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sorry

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tryna understand this vector thing

young spindle
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you have an exam soon or something

old pasture
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LOL

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kinda

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answer the easiest question for u

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among all things i sent

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do i need to do guassian method here

young spindle
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yeah

maiden terrace
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@old pasture are you in a linear algebra class or are you just self-learning?

old pasture
old pasture
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vectors and stuff

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ik guassian and all that

maiden terrace
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I'm a reading type learner. I find that watching a video makes it too easy to stop paying attention, then you retain nothing.

old pasture
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I understand by examples fast

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I could learn by reading but my english isnt perfect so if I dont know 1 word it will all be confusing

young spindle
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what's your native language ?

old pasture
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russian

young spindle
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aight idk russian can't really help finding texts in russian

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but if your exam is in english you prolly want to know the english terms tho

old pasture
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what the topic name

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i will search videos

old pasture
young spindle
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linear algebra

old pasture
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no

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that specific

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vector

young spindle
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what do you mean

old pasture
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nothing