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Questions tagged [gaussian-elimination]

For questions on or related to the technique of Gaussian elimination, used in solving systems of linear equations.

For questions on or related to the technique of Gaussian elimination (also known as row reduction), used in solving systems of linear equations. Gaussian elimination is an algorithm for solving such systems. It is generally seen as a sequence of operations performed on the corresponding matrix of coefficients. These operations are:

  1. swapping two rows;
  2. multiplying a row by a non-zero number;
  3. adding a multiple of one row to another row.

Gaussian elimination can also be used to find the rank of a matrix, to compute the determinant of a matrix, and to determine the inverse of an invertible square matrix. It is named after Carl Friedrich Gauss (1777–1855).

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Is there any sufficient or necessary conditions for a matrix to do Gaussian Elimination?

For now I know that we can do Gaussian elimination to $ m\times n $ matrices. But is there any restrictions?
Malith
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Gaussian Elimination: 4 equations, 8 unknowns

I need to find the solution set of all b=(b1,b2,b3,b4) element R^4 for this: I know how Gaussian elimination works, but how do I find all possible solutions of all the b's?
user3071205
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Do pivots have to be consecutive across the columns or can their be a break?

I have a 3x3 matrix as described below. Is the rank of this matrix 1 or 2? Or otherwise asked, is it okay to have "gaps" in the pivots across the columns? $$ \left(\begin{array}{cc} 1 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ \end{array}\right) $$
Bryon
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Can I get this Gaussian elimination solution correct?

I have "Linear Algebra an introduction" ed 2 by A.O.Morris open in front of me at Exercise 1.2 (vi): "Find the reduced echelon matrix of: $\begin {pmatrix} 1 & 1 - \sqrt 2 & 0 & \sqrt 2 \\ \sqrt 2 & -3 …
Prime Mover
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results of a guassian elimination and what they mean

Hey guys I was wondering if someone could tell me what each of the different scenarios of a guassian elimination mean. (3 equations) e.g. one row of $0$ means that its a line in $R^3$ (I think) What would the result of the elimination look like if…
Mathlete
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Is it allowed to swap 2 columns in gaussian elimination?

I am trying to find inverse of a matrix I know swapping two rows is fine but what about columns ?
Endrit Shabani
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Gaussian elimination involving parameters

The problem is :Solve the given system of equations involving the parameter a : $$x+y+az=1\\ x+ay+z=a\\ ax+y+z=a^2\\ ax+ay+az=a^3 .$$ I tried to solve this using the Gaussian method but I'm stuck because this is $4\times3$ matrix, and the Gaussian…
Anthony
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i have a problem solving a system with gauss method (elimination).

My teacher said I have to solve it with gauss method, I tried to make for example $0y$ but I can't come to the result. If someone can help me I would appreciate that. $$2x+z=7$$ $$x+y=2$$ $$y-z=-2$$ I did like this: $$2x+0y+z=7$$ …
dona12
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whether the Gaussian elimination method could be used to solve for $p,q,r$?

could anyone tell me whether the Gaussian elimination method could be used to solve for $p,q,r$? $$2p+3q-r=3\\p-q+2r=-1\\ p+0\times q+3r=2$$ Thanks so much for any help.
Myshkin
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Row echelon form except last row. Necessary to proceed with gaussian algorithm?

Suppose we were given the following matrix (I made up the numbers). The first and second row are in row echelon form. However the third is not. Do we still need to put the third row in row echelon form even if we can see that 1 * x = 2, which we…
CuriousIndeed
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Can Gaussian elimination find a zero vector when $m < n$?

Given $m$ rows with $n$ variables where $m < n$, and given that there exists a combination of some of the rows that gives a zero vector. Is it promised when computing the reduced-row echelon form, with Gaussian elimination to find a zero…
Ilya Gazman
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Can Gaussian elimination fail finding null space?

Is it possible to have $m$ rows with $n$ variables over F2, where $m < n$ that will have some combination of rows that can form a zero vector, but there will be no zero vectors in reduced-row echelon form? Please provide an example of such a setup…
Ilya Gazman
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solve 6 equations with 6 unknowns Gauss

I have been using the finite-difference method and get 6 equations with 6 unknowns. Now I want to solve them using Gauss' method but I don't know how. I can solve them with math-lab but I want to learn Gauss'…
Red0ne
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determine general solution for this linear system

lateX of linear system to view more clearly I have find a general solution to this linear system (included a link to lateX pic): x_1 - 2x_2 + x_3 - 3x_4 = 1 2x_1 - 4x_2 + 4x_3 + 6x_4 + 4x_5 = 6 -2x_1 + 4x_2 - x_3 - 6x_4 + 2x_5 = 0 1x_1 - 2x_2 -…
Chelsea777
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Gauss-Jordan elimination to solve without employing pivoting

While reading the book Numerical Methods for Engineers by Steven Chapra and Raymond Canale, I came across a problem in Gauss-Jordan elimination. The problem says, $$2x_1+x_2-x_3=1\\ 5x_1+2x_2-2x_3=-4\\ 3x_1+x_2+x_3=5$$ to solve…
sphoenix
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