What is Elimination: Definition and 163 Discussions
An elimination reaction is a type of organic reaction in which two substituents are removed from a molecule in either a one- or two-step mechanism. The one-step mechanism is known as the E2 reaction, and the two-step mechanism is known as the E1 reaction. The numbers refer not to the number of steps in the mechanism, but rather to the kinetics of the reaction: E2 is bimolecular (second-order) while E1 is unimolecular (first-order). In cases where the molecule is able to stabilize an anion but possesses a poor leaving group, a third type of reaction, E1CB, exists. Finally, the pyrolysis of xanthate and acetate esters proceed through an "internal" elimination mechanism, the Ei mechanism.
For this problem,
For (i) the solution is,
However, I am somewhat confused how to follow the steps of the Gauss-Jordan Elimination algorithm from there. Do I have to eliminate the coefficients from ##x_2## and ##x_3## respectively from row 1 and the -5 coefficient from row 2 in the exact...
Hi! Please, could you help me on how to solve the following matrix ?
I need to replace the value 3 on the third line by 0, the first column need to remain zero and 1 for the third column. I'm having a lot of difficulties with this. How would you proceed ?
Thank you for your time and help...
Part (A): The matrix is a singular matrix because the determinant is 0 with my calculator.
Part (B): Once I perform Gauss Elimination with my pivot being 0.6 I arrive at the last row of matrix entries which are just 0's. So would this be why Gauss Elimination for partial pivoting fails for this...
Hey,
I have this equation in which I have to determine its reaction mechanism.
I managed to determine how we managed to obtain this the molecule in the picture above, but I don't understand the mechanism behind obtaining the second alkene. Thank you so much for your help, and sorry if the...
I would to know if I'm solving system differential equation by elimination correctly. Could somebody check my sample task and tell if something is wrong?
I don't know the terms so I'm sorry if the informations at summary above is unclear. But I add a detailed photo of my calculations below. I use Gauss' Elimination laws.
So, my wife and I really like our new house, but after living in it for two months we desire to find a smart way to deaden the noise. You see, our previous house was smaller, had carpet mostly, and did not reflect the noise inside near as much as this new house. Our new house is larger, has...
Hi,
I ask for a clarification about the following: consider for instance a 10 x 12 homogeneous linear system and perform Gauss elimination for the first 8 unknowns. Suppose you end up with 5 equations in the remaining 12-8 = 4 unknowns (because in the process of the first 8 unknowns elimination...
Hi,
I've the following doubt: consider an homogeneous linear system ##Ax=0## with ##A## a singular square matrix.
The resulting matrix attained through Gaussian elimination will be in upper triangular or raw echelon form ?
Thanks.
Homework Statement
I just have a problem with (A) & (B)
The attempt at a solution
Analysing all possible products;
(A) can give 1-pentene (minor) + 2-pentene (major). But you also have the E-Z diastereomers of 2-pentene. So that's total 3 possible products.
(B) will give only the...
Homework Statement
*How many halogens will be removed in the following E2 reactions combined?*
The Attempt at a Solution
The question's language isn't error free. So, looking at the options, assuming it's *How many halogens will be removed in the following E2 reactions combined?*, the chair...
Homework Statement
When trans-2-methylcyclohexanol is subjected to acid-catalyzed dehydration, the major product is 1-methylcyclohexene.
However, when trans-1-bromo-2-methylcyclohexane is subjected to dehydrohalogenation, the major product is 3-methylcyclohexene.
The attempt at a solution...
It's a problem of reducing an abrupt shock load as an 850 kg runaway machine trundles down ramps, and comes to an abrupt halt at the end of its tether fixed to a van's tow hitch. Ramps fixed to the van's rear door sill incline at 20 degrees to ground level and their length is 2.5 metres. I...
Can anyone help me with this ?
What does the arrow mean ? Is it cis or trans,the base is small so it should be an E2 elimination with zaitsev product.Though I think it may be due to the beta hydrogen being unavailable,but I do not know whether the arrow means from the upper or lower /cis trans...
Hi, I have derived a matrix from a system of ODE, and the matrix looked pretty bad at first. Then recently, I tried the Gauss elimination, followed by the exponential application on the matrix (e^[A]) and after another Gauss elimination, it turned "down" to the Identity matrix. This is awfully...
Homework Statement
Given this matrix:
I am asked to find values of the coefficient of the second value of the third row that would make it impossible to proceed and make elimination break down.
Homework Equations
Gaussian elimination methods I used given here...
Post moved by moderator from Homework section
Hello, I was curious as to why Gaussian elimination works. I know that if we have two ( or more) systems of two (or more) linear equations, we can write then in terms of a matrix. However, what does it mean when I get the identity on the left hand...
I am fairly new here so I apologize for any mistakes in my post.
My question concerning solving a system of equations using Gauss-Jordan Elimination is specifically about different ways to handle a possible constant. Say for instance you have three equations:
X1+X2+X3 + 3 = 9
2X1+4X2+X3 =...
If we suppose there is an algorithm for P vs NP, would it have to be able to find solutions where we now use trial and error? In harder Sudokus, for example, there are times when you have two or more possible numbers and need to guess whereafter you work the rest of the numbers through to see if...
1. G is chordal iff G has a Perfect Elimination Scheme/Ordering (PES)
2. G is chordal iff every induced subgraph H of G has a simplicial vertex in H.
I want to show directly (ie, don't use the above) to show that G has a PES iff every induced subgraph H of G has a simplicial vertex.
(->)...
Homework Statement
x1 + 2x2 = 9 ,
6x1 + 6x2 -8x3 = 1 ,
-3x2 +x3 = 0 [/B]
Here's a question from my book . I'm asked to find the x1 , x2 and x3 by using the gaussian elimination with pivoting .Homework EquationsThe Attempt at a Solution
Pls refer to this thread for the lecturer's method...
Homework Statement
In my book , the author stated that when we do the pivoting , we need to make the element below the leading element = 0 . For example for 3x3 matrix , for the first column , we have to make a11 = max , and make sure that a21 and a31 less than a11 , for the second column , we...
Homework Statement
I am asked to solve this question using pivoting technique ... so , in I , I switched the R1 and R2 so that a11 is max , in III , i switched R9 nad R10 , so that a22 is max . But , in IV , i found that the a31 become -2/9 , which is not 0 anymore , what's wrong with my...
Homework Statement
system of equations is as follows
4x +2y -2z = 0
2x + y -z= 1
3x +y -2z = 1
Homework EquationsThe Attempt at a Solution
[/B]
Using gaussian elimination
we can multiply mid-eq, by (-2) [[[actually... it is simply a basic equation procedure]]]
2x+y-z=1 |*(-2)
=
-4x -2y...
Dear forum,
I'm new here (living in Arizona). I am stuck getting to derive this:
F1−F2−F3 = 0, (2.1)
F1c1−F2c2−F3c3 = 0, (2.2)
F1z1−F2z2−F3z3 = 0. (2.3)
Where the only unknowns are F2 and F3. The textbook states that F1, F2 and F3 can be eliminated to get:
c1z3 −c1z2+c2z1 −c2z3 −c3z1 +c2z2 =...
Homework Statement
I feel like I should know the answer to this, so I believe this to be an easy question. Say have matrix A, and I store the elimination matrices E_1,1 E_2,1 etc. and somewhere in the elimination process I have to use a permutation matrix to swap rows. My question is when I...
I'm not sure where you're getting the idea that z = 2, as this is not correct.
I'm assuming this is to be done without pivoting...
Set up your augmented matrix:
$\displaystyle \begin{align*} \left[ \begin{matrix} 2 & \phantom{-}1 & -3 & -5 \\ 1 & -1 & \phantom{-}2 & 12 \\ 7 & -2 & \phantom{-}...
Homework Statement
I started with the following equations :
3w+2x+3y+z=76
w+2x+2y+z=59
w/2+x+y+z/4=21
Homework Equations
Gaussian elimination
The Attempt at a Solution
So I got the following after applying Gauss' method :
3w+2x+3y+z=76
-4x-3y-2z=-101
3/2z=51
which gives z=34
Then I get...
Hey! :o
Let $L=\{+, ' , 0, 1, T, C\}$ be the language where $ ' : \frac{d}{dz}$, $T(x) \Leftrightarrow x \notin \mathbb{C}$ (so $x$ is not constant), $C(x) \Leftrightarrow x \in \mathbb{C}$ (so $x$ is constant)
$x, f, g \in \mathbb{C}[z, e^{\lambda z } \mid \lambda \in \mathbb{C}]. $
(In...
Hey! :o
Say that we work in a language $L$.
A theory $T$ (i.e. a subject of the set of formulas) of $L$ admits elimination of quantifiers if any $L$-formula $\phi (x)$ is equivalent in $T$ to an existential formula.
Let $T$ be an $L$-theory.
Assume that any formula of the form $\exists x \ \...
Hey! :o
I am looking at the elimination of quantifiers.
Let $T(x)$ be the predicate that $x$ is non-constant.
Consider the expression $$\exists x \left (x'+x=1 \land T(x) \right ) \tag 1$$
Since the solution of the differential equation $x'+x=1$ is $x(t)=1-Ce^{-t}$, we can eliminate the...
This is actually a pretty simple thing, but the ref(A) that I compute on paper is different from the ref(A) that my TI-89 gives me.
Compute ref(A) where A =
\begin{bmatrix}
1 & 2\\
3 & 8
\end{bmatrix}
\\ \begin{bmatrix}1 & 2\\ 3 & 8\end{bmatrix} \ r_2 \rightarrow r_2 - 3 \times r_1 \\ \\...
This reminds me of the old mastermind puzzle.
Computer picks (at random) a 4-digit number.
The number will contain only the digits 1, 2, 3, and 4:
the digits may be used more than once: 1111 to 4444.
You input a guess as to what the number is.
If your guess has at least 3 digits in their...
I am attempting to find the determinant using gaussian elimination for the following matrix [4 3 2; 1 7 8; 3 9 3].
I have begun by attempting to form zeros below the diagonal. The answer should be -165, however i keep getting values up to -665. I have tried a variety of times and keep getting...
I attempting to find the determinant using gaussian elimination for the following matrix [1 2 3; 3 2 2; 0 9 8].
I have begun by attempting to form zeros below the diagonal. My first row operation was to make row 2 equal to 3(row 1) - row 2. This gives me [1 2 3; 0 4 7; 0 9 8] . I think i am...
Homework Statement
I have this problem:
I known that reaction with TsOH would replace -OH groups with TsO (substitution reaction). (Et)3N would therefore act as a base to abstract H to form an alkene. The problem is i know it should be an E1cb reaction but how do I obtain an alkene? I tried to...
Hello everyone, I have another question mark buzzing inside my head.
After the elimination steps of a matrix, I'm having some problems about imagining in 3D.
For example, x=t , y=2t, z=3t what it shows us?
Or, x=t+2, y=t,,z=t ?
Or another examples you can think of. ( Complicated ones of...
If I switch 2 rows, do I have to multiple by -1 each time?
For example, I have
If I switch row 2 and 3, will it become this:
Or this?
Each time I make a switch, do I have to also put a negative sign?
Edit: Not really related to Gaussian elimination, but this is from a Gaussian...
Hello. Nice to meet you. I have just enrolled. :)
I knew how to solve and to find out inverse Matrix by using Gaussian elimination.
However, I was wondering why AI -> IA' is satisfactory.
In my university, I was just taught how to use but wasn't taught why it is satisfactory.
Thank you for...
When is an Elimination 2 reaction more likely to take place than any other reaction (more likely than SN1, SN2, E1)? Details and examples welcome.
I'm reviewing this for a student I'm tutoring and seem to have forgotten what makes E2 happen over the other reactions. Thanks!
Use Gaussian elimination with back substitution to solve the following system:
x1+x2+x3=1,
x1+2x2+2x3=1,
x1+2x2+3x3=1.
The answer is (1, 0, 0) and I know how to solve the problem but I just don't know if I should use bracket or the big parentheses for this type of problem when I solve...
x^2-13xy+12y^2=0 (1)
x^2+xy=156 (2)
What I have so far:
x^2+xy=156
xy=156-x^2
y=(156-x^2)/x)
Plugged y=(156-x^2)/x) into (1):
x^2-13x(156-x^2)/x)+12(156-x^2)/x)^2=0
For 1st half I Multiplied x to -13x in order to get the same denominator so I can multiply it to (156-x^2)/x)...
Homework Statement
Find the differential equation of ln y = ax^2 + bx + c by eliminating the arbitrary constants a, b and c.
Homework Equations
Wrosnkian determinant.
The Attempt at a Solution
I've solved a similar problem (y=ax^2+bx+c --> y'''=0), but couldn't do the same with...