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#761 ExidsJarofJamsI.M

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Posted 08 September 2017 - 03:30 AM

1) I think you mean to ask what happens to Fe2+; it is reduced. Just remember "LEO the lion says GER"; Losing Electrons is Oxidation, Gaining Electrons is Reduction. Since the Fe2+ ion gains two electrons becoming a neutral Fe atom in the process, it is reduced.

2) Here, you should remember "AN OX, RED CAT". That is, oxidation occurs at the anode and reduction occurs at the cathode. The cobalt electrode is having its Co atoms dissolve into Co2+ ions, which means that they are losing electrons, or being oxidized. So the cobalt electrode is the anode.


Omg thanks! I actually says Fe... so it would its neutralize?
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#762 Guardian of the Galaxy

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Posted 08 September 2017 - 04:14 AM

Omg thanks! I actually says Fe... so it would its neutralize?

 

That's a poorly written question then, since Fe is the result of the reaction. It still sounds to me like they want you to recognize that it is a reduction reaction taking place.


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#763 metaphorical penis

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Posted 10 September 2017 - 12:16 AM

do you find the determinant of elementary matrices by multiplying the diagonal altogether or is there more to it

 

im trying to look at my book and the theorem makes no sense to me

 

 

like this 

0 0 0 1 | 

0 1 0 0 |                  

0 0 1 0 | 

0 0 0 1 |

like why is dete(a) = -1


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#764 ExidsJarofJamsI.M

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Posted 11 September 2017 - 12:54 AM

That's a poorly written question then, since Fe is the result of the reaction. It still sounds to me like they want you to recognize that it is a reduction reaction taking place.

thanks ! theyre correct


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#765 Guardian of the Galaxy

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Posted 11 September 2017 - 01:01 AM

do you find the determinant of elementary matrices by multiplying the diagonal altogether or is there more to it

 

im trying to look at my book and the theorem makes no sense to me

 

 

like this 

0 0 0 1 | 

0 1 0 0 |                  

0 0 1 0 | 

0 0 0 1 |

like why is dete(a) = -1

 

Is that last row supposed to have the 1 on the left? This summarizes the determinants of elementary functions. I just looked at the proofs for these in my lin alg notes from a couple of years ago and they're really quite tedious...


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#766 metaphorical penis

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Posted 11 September 2017 - 06:27 PM

Is that last row supposed to have the 1 on the left? This summarizes the determinants of elementary functions. I just looked at the proofs for these in my lin alg notes from a couple of years ago and they're really quite tedious...

Oops i wrote it wrong yeah a31 is supposed to be 1

So its pretty much -1 bc you have to switch the rows right?
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#767 Guardian of the Galaxy

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Posted 11 September 2017 - 11:42 PM

Oops i wrote it wrong yeah a31 is supposed to be 1

So its pretty much -1 bc you have to switch the rows right?

 

Yes, it's the third type of elementary matrix listed


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#768 metaphorical penis

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Posted 01 October 2017 - 10:47 AM

Spoiler

 

how do i do #22


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#769 ExidsJarofJamsI.M

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Posted 04 October 2017 - 07:30 PM (Edited by ExidsJarofJamsI.M, 06 October 2017 - 02:59 AM.)

.
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#770 brumalParty

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Posted 16 October 2017 - 03:38 PM (Edited by brumalParty, 18 October 2017 - 06:24 AM.)

 

how do i do #22

Do you still need help with this? You may have figured it out by now since it follows the same method with the question 23.

>>Just in case, for any vector u and v, for the two to be parallel means v can be written as u=k x v.(for k any complex number, furthermore for any k in any field F) (I have used x for the multiplication sign and in matrix ; means the row ended that is if A=[1 2; 3 4] , first row of A from left to right is 1 and 2 and the second row is 3 and 4)

>>In your question for v = (8t, -2), k must be 1/2 since (k x (-2) = -1). Since k is 1/2=> 4 = 1/2 x 8t => t = 1. Hence in (a) they are parallel for t = 1.

>>(b) v = (8t, 2t). 4 = k x 8t => k x t = 1/2 and -1 = k x 2t => k x t = -1/2. But 1/2 is not equal to -1/2 so they are never parallel.

>>© v = (1, t2) => 4 = k x 1 = k, Since k is 4, -1 = 4 x t2 Hence they would be parallel for the complex numbers i/2 and -i/2 (Usually in algebra courses you would be allowed to use complex numbers but you should still check if you are allowed to use them. If you are not allowed to use them, they are never parallel, again)

Also for determinant, (pass this part if you are not interested in abstract linear algebra) determinant is defined as for a matrix A, (there should be permutations under Σ, since you want to sum all of the permutations up to isomorphism possible) detA=Σ(sgn(j1....jn)a1j1 a1j2 .... anjn) where aijn denotes the element in the ith row and jnth column (jn is a permutation so it's not the same as the initial column number j) and the sgn(j1....jn) denotes the -1 to the power of number of permutations of elements 1,2,...,n to j1....j(if you haven't taken any algebra course before, this is simply just saying the number of ways you can correctly and uniquely permute (1,2,...,n),,,, up to isomorphism of course) and defined as (-1)number of inversions in j1....jn (>>further (-1)row num+col num in the determinant comes from this sign of permutation)

 

Moving on/further from the abstract definition for a 2x2 matrix A=[a b; c d] , det(A) = ad-bc  (coming from definition sgn(1,2)a11a12 + sgn(2,1)a12a21) (However, I still used the definition)

 

We can use the definition to calculate the determinant of any matrix using the determinant of the 2x2 matrix which is above and would usually be given to you as a lemma (but it's a simple application of the definition),

for B=[a b c; d e f; g h i] I will use the first row to calculate the determinant however you are free to choose any row you like

det(B)=(-1)1+1a det([e f; h i]) + (-1)1+2b det([d f; g i]) + (-1)1+3c det([d e; g h]). (However, I still used the definition)

 

That is, you are first choosing a row then by starting from the first column, you will add the column number and the row number (this is the number of permutations) and you will calculate-1 to the power of sum you have just calculated then you will multiply it with the rest: and then you will multiply by the element which is in the intersection of the row and column you are currently in then you will disregard all the elements in the row and column you are currently in, then you will multiply by the determinant of the smaller matrix created by disregarding that row and column. Then you will move on to the next column and continue the process until the end of the row. For the new determinants you have to calculate, you have to continue this process until you get to the matrix in the form 2x2.

 

But since the abstract definition is practically useless there are some correlations and shortcuts which can help you calculate the determinants more easily, I suggest you to study them. Your teacher can probably help you. It's really easy actually, it just takes lots of works to actually use the determinant practically. If you have more questions about how to calculate them or how to prove their properties, I would love to help ^^

 

 

NOTE: Furthermore for question 22, CLAIM: for vectors u=(x1, y1) and v=(x2, y2), (assuming u and v are not the zero vector) they are said to be parallel if and only if the determinant of the matrix A = [x1, y1; x2, y2] is zero.

>>proof: if u and v are parallel then u = k x v for some k in a field. then u can be written as (kx2, ky2)

then det(A) = x1y- y1x= kx2y2 - ky2x2 = 0

if det(A) = 0 then x1y2 = y1x2 => x1/x2 = y1/y= k for some k in a field. Hence the vectors are parallel.

 

Applying the claim to your question:

(a) det([4  -1; 8t  -2]) = -8 - (-8t) = 8t - 8 Since we want u and (a) to be parallel determinant must be zero and 8t-8 is zero when t = 1.

(b)det([4  -1; 8t  2t]) = 8t - (-8t) = 16t Since we want u and (b) to be parallel determinant must be zero and 16t = 0 when t = 0 but if one of the vectors is zero then the definition fails and the vectors are not parallel.

©det([4  -1; 1 t2) = 4t2 - (-1) = 4t2 + 1 Since we want u and © to be parallel determinant must be zero. 4t2 + 1 = 0 then 4t2 = -1 then t= -1/4 if you take the square root you will get two roots in complex numbers that are i/2 and -i/2. So the vectors are parallel for t = i/2 or t = -i/2

 

 

!!When I first posted this, I have made many mistakes but currently everything seems fine.!!


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#771 Nev Schulman

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Posted 25 October 2017 - 11:23 AM

people of oh who have been to Thailand please help

https://onehallyu.co...en-to-thailand/


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#772 Pananana

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Posted 20 November 2017 - 09:17 AM

Can somebody help me with organic chemistry? I need a full mechanism of catalytic hydrogenation of aromatic rings.


I'm uni student btw getting a course of medical technology major in clinical chemistry
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#773 mynameiswonho

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Posted Today, 10:45 AM

I FORGOT THIS THREAD EXISTS. GUYS PLEASE HELP ME. OH MY GOD.

I have a survey I need to do for my final project, please help me by responding (if you live in the US)

It is about leisure and I will be using it to find data to help my argument on the relationship between children and institutions SAVE ME PLEASE

https://www.statcrun...9117&code=PJUOC


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