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.

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  1. C

    Gauss-Jordan Elimination algorithm steps

    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...
  2. R

    B Row reduction, Gaussian Elimination on augmented matrix

    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...
  3. V

    Gaussian Elimination of Singular Matrix with partial pivoting

    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...
  4. duchuy

    Chemistry Are there alternative hydrogen abstraction pathways in E2 elimination reactions?

    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...
  5. P

    I Solving a system of differential equations by elimination

    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?
  6. R

    I This linear system has a solution? (Gauss' elimination)

    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.
  7. CPW

    Misc. Getting used to new house, but what's best for noise elimination?

    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...
  8. cianfa72

    I Gaussian elimination for homogeneous linear systems

    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...
  9. cianfa72

    I Gaussian elimination for a singular square matrix

    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.
  10. baldbrain

    Eliminating Alcohols: Why Do (A) and (B) Give Different Products?

    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...
  11. baldbrain

    How many halogens will be removed in the E2 reactions combined?

    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...
  12. baldbrain

    Elimination reactions of cyclohexane derivatives

    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...
  13. Emellish

    Elimination OF Abrupt Mechanical Shock Loading

    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...
  14. C

    Understanding the Arrow Notation in Organic Chemistry Elimination

    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...
  15. S

    I Consequences on a system of ODEs after performing operations

    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...
  16. M

    Coefficients that make Gaussian elimination impossible?

    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...
  17. M

    Why does Gaussian elimination work?

    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...
  18. Oannes

    I Solving System of Equations w/ Gauss-Jordan Elimination

    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 =...
  19. A

    A P vs NP Guessing and process of elimination

    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...
  20. M

    MHB Chordal graphs and perfect elimination orderings

    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. (->)...
  21. F

    Pivoting (Gaussian elimination)

    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...
  22. F

    Gaussian elimination (pivoting)

    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...
  23. F

    Solve Gaussian Elimination w/Pivoting: Problem Explained

    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...
  24. L

    Gaussian elimination system of Eqs, the case of no solution

    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...
  25. B

    I Simplifying 3 simultaneous equation into one equation

    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 =...
  26. Y

    Linear Algebra - Elimination Matrix when Permutation Needed

    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...
  27. P

    MHB James' question about Gaussian Elimination

    We start by writing the system as an augmented matrix $\displaystyle \begin{align*} \left[ \begin{matrix} 2 & -2 & 1 & 1 & \phantom{-}4 \\ 4 & -1 & 2 & 3 & -\frac{5}{2} \\ 4 & -4 & 5 & 1 & \phantom{-}8 \\ 0 & \phantom{-}2 & 3 & 4 & -5 \end{matrix} \right] \end{align*}$ Once we have used...
  28. P

    MHB Solve System w/ Gaussian Elimination & Partial Pivoting (Sufyan)

    We write the system as an augmented matrix $\displaystyle \begin{align*} \left[ \begin{matrix} \phantom{-}1 & 4 & \phantom{-}1 & 0 & \phantom{-}5 \\ \phantom{-}1 & 6 & -1 & 4 & \phantom{-}7 \\ -1 & 2 & -9 & 2 & -9 \\ \phantom{-}0 & 1 & \phantom{-}2 & 0 & \phantom{-}4 \end{matrix} \right]...
  29. P

    MHB Question from Jesse about Gaussian Elimination and LU factorisation.

    This system can be written as a matrix equation $\displaystyle \begin{align*} A\,\mathbf{x} = \mathbf{b} \end{align*}$ as $\displaystyle \begin{align*} \left[ \begin{matrix} \phantom{-}2 & 4 & \phantom{-}0 & 1 \\ \phantom{-}2 & 8 & -2 & 7 \\ -2 & 2 & -2 & 7 \\ \phantom{-}0 & 8 & -5 & 11...
  30. P

    MHB Question from Kamal about Gaussian Elimination via email

    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{-}...
  31. P

    Gaussian Elimination: Solving Homework Problem

    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...
  32. A

    Can Gauss-Jordan Elimination simplify a matrix into a reduced row echelon form?

    By using row operation, how can ## \left( \begin{array}{rrrr|r} 2 & 0 & -1 & 0 & 0 \\ 6 & 0 & 0 & -2 & 0 \\ 0 & 2 & -2 & -1 & 0 \end{array} \right) ## be ## \left( \begin{array}{rrrr|r} 1 & 0 & 0 & -\frac{1}{3} & 0 \\ 0 & 1 & 0 & -\frac{7}{6} & 0 \\ 0 & 0 & 1 & -\frac{2}{3} & 0 \end{array}...
  33. M

    MHB Quantifier Elimination: Proving Without Variables

    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...
  34. M

    MHB T admits elimination of quantifiers

    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 \ \...
  35. M

    MHB Elimination of quantifiers

    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...
  36. kostoglotov

    Is this the correct way to compute the row echelon form?

    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 \\ \\...
  37. W

    MHB Minimum Guesses to Solve Mastermind Puzzle w/ 4 Digits

    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...
  38. B

    MHB Determinant using gaussian elimination

    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...
  39. B

    MHB Help with finding the determinant using gaussian elimination

    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...
  40. T

    Organic Chemistry - Elimination/substitution

    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...
  41. K

    The geometric shape of parametric equations

    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...
  42. D

    Solving a Matrix with Elimination: Inputting the Right Number of Values

    Homework Statement #include <stdio.h> #include <stdlib.h> #include <math.h> int main() { int i,j,k,n; float A[3][4]; float x[3],c,sum=0; n=2; printf("first row\n"); scanf("%f",&A[0][0]); scanf("%f",&A[0][1]); scanf("%f\n",&A[0][2]); printf("second row\n")...
  43. P

    Finding determinant through Gaussian elimination

    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...
  44. T

    Books on adiabatic elimination

    Hi, What books/book chapters are good for learning adiabatic elimination in great depth? Thank you.
  45. S

    Finding Inverse of Matrix by using Gaussian-Jordan Elimination

    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...
  46. gauss44

    When is an Elimination 2 reaction more likely to take place?

    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!
  47. M

    Use Gaussian elimination with back substitution?

    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...
  48. H

    MHB Solving System of Equations using Substitution or Elimination

    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)...
  49. JasonHathaway

    Differential equations: Elimination of arbitrary constants

    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...