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

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0
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1answer
23 views

Solve this equation 3x3 using Gauss-Jordan

I have this problem: With this system, determine the values of $K$ to the system have: a) One only solution b) Don`t have solution c) Infinite solutions $x-3z=-3$ $2x+Ky-z=-2$ $x+2y+Kz=1$ How do ...
-4
votes
1answer
30 views

What is the reduced row echelon form of A?

let $A = \left( \begin{array}{cccc} 7 & 7 & 9 & -17\\ 6 & 6 & 1 & -2 \\ -12 & -12 & -27 & 1 \\ 7& 7 & 17 & -15\end{array} \right)$ What is the reduced ...
1
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1answer
29 views

Solution to two equations with three unknowns

So I'm a student studying through correspondence and I need some help. This is an assignment question, and I have tried everything I know how, to answer it which has lead me to the conclusion that ...
0
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1answer
45 views

Difficulty with Gaussian Elimination involving a,b coefficients

I have the system matrix as follows: {1 2 2 1 1 a 3 3 1 11 a b} I am attempting to row reduce this matrix, but am having difficulty in this process, particularly with Row 3. I ...
0
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0answers
23 views

Gaussian Elimination method with respect to maximum XOR subset problem?

Can anyone explain me Gaussian Elimination method with respect to maximum XOR subset problem? I am not able to figure out the various posts posted on Internet of the above solution. So I am ...
0
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0answers
27 views

Is the U factor in LU decomposition for rectangular matrices always in row echelon form?

I have come across the following rectangular 5 x 10 matrix and carried out a LU decomposition of it, in the form PA = LU. The following matrices were obtained by function scipy.linalg.lu from module ...
0
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1answer
43 views

Solving 2x2 diagonally dominant matrix systems (non-symmetric)

I have a linear system of the form $Ax=b$ where $A\in \mathbb{R}^{2\times2}, b\in \mathbb{R}^{2\times1}$. A is diagonally dominant and non-symmetric. This is a "kernel" that I am using to solve a ...
2
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1answer
37 views

Gauss Seidel Method - How do I avoid calculating $L^{-1}$?

I'm trying to write a matlab code that gets a diagonal dominant matrix $A$, vector $b$, and finds an approximate solution $x$ to $Ax=b$ using Gauss-Seidel Method. I understand the theory. Suppose ...
0
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0answers
17 views

Low pass filter to maintain edge information

I am looking for a kernel as low pass filter that satisfy as:I must find a kernel that statisfies as follows: In the my reference paper, the author suggest gaussian kernel that is The gaussian ...
0
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2answers
45 views

Which is kernel similar gaussian kernel?

I must find a kernel that statisfies as follows: In the my reference paper, the author suggest gaussian kernel that is The purpose of that kernel is that it will take a weight for each points ...
1
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2answers
47 views

Why use Gauss Jordan Elimination instead of Gaussian Elimination, Differences

Why use Gaussian Elimination instead of Gauss Jordan Elimination and vice versa for solving systems of linear equations? What are the differences, benefits of each, etc.? I've just been solving ...
0
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1answer
30 views

Linear Transforms & Matrices

$T:R^4 -> R^3$ Linear Transform This matrix is $[T]_{B2}^{B1}$ = A =\begin{pmatrix}1&2&3&4\\1&4&0&2\\2&2&9&10\end{pmatrix} After elimination we get: ...
-2
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2answers
28 views

Solving Linear equation Gaussian method of elimination [closed]

Solving linear equation Gaussian method of elimination $$\left\{ \eqalign{ -x-y & =7 \\ 4x-y & =-3 } ...
0
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1answer
23 views

Linear Algebra - elimination and linear systems

By given this matrix: \begin{pmatrix}1&1&1&0\\2&3&k&1\\3&k&5&1\end{pmatrix} I need to find, what are the values of k the system has infinity/single/no solution. So ...
0
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0answers
23 views

Gaussian Elimination diagonal elements

For a matrix A, assume that B is the upper triangular matrix after applying Gaussian elimination on A. I want to calculate only the diagonal elements of the output matrix B in terms of $A_{ij}$ (the ...
1
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0answers
23 views

Gaussian elimination vs. Jacobi iteration

How can I determine which of the matrix solver is faster for a given set of equations: Gaussian elimination or Jacobi iteration? In case, I have a banded matrix, is it advisable to use LU ...
3
votes
4answers
104 views

Can you use row and column operations interchangeably?

Is it possible to use row and column operations "at the same time" on a matrix $A$? So, for example, first subtracting $row_1$ from $row_2$, and then choosing to multiply $column_3$ by a constant $c$? ...
0
votes
1answer
29 views

Gaussian elimination easily?

Let $$\left( {\matrix{ 1 & 0 & { - 3} \cr 0 & 2 & {\lambda + 3} \cr 0 & 0 & {5 - {\lambda ^2}/2 - 3\lambda /2} \cr } \left| {\matrix{ { - 3} \cr 2 ...
0
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1answer
32 views

Gauss-Jordan Method

I keep getting the wrong set of solutions can someone help me. I know that when using the Gauss-Jordan method, the rules that I must follow can be applied in a variety of different procedures then why ...
0
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1answer
25 views

Calculating the rank of two given matrices

I read somewhere that the rank of a matrix is the number of its nonzero rows or columns after Gaussian elimination. In the following matrices, how should I know Gaussian elimination is done? They are ...
1
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1answer
28 views

Specific system of equations with multiplications

I'm facing a math problem that I thought easy, but I'm stuck with a solution that doesn't seem optimal. The problem is the following : I have "registers" which are the expanded representation of ...
0
votes
2answers
74 views

how to solve a 4x5 matrix with guassian elimination or gaussian-jordan

$$ \left[ \begin{array}{ccccc} 2 & -1 & 3 & 4 & 9 \\ 1 & 0 & -2 & 7 & 11 \\ 3 &-3 & 1 & 5 & 8 \\ 2 & 1 & 4 & 4 & 10 \\ ...
1
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2answers
24 views

Get variables with Matrix

I try to get the variables for this equation: $$\begin{cases} 6x_1 + 4x_2 + 8x_3 + 17x_4 &= -20\\ 3x_1 + 2x_2 + 5x_3 + 8x_4 &= -8\\ 3x_1 + 2x_2 + 7x_3 + 7x_4 &= -4\\ 0x_1 + 0x_2 + 2x_3 ...
0
votes
1answer
21 views

Get variables with Gauß

I try to find the solutions for the following expression with the Gauß Formula: $$1x_1-1x_2+3x_3=0$$ $$2x_1 + 3x_2 - 1x_3 = 0$$ $$3x_1+7x_2-5x_3 =0$$ So i started: $ \begin{pmatrix} ...
0
votes
2answers
37 views

Method for Finding Matrix-Inverse Through Gauss-Jordan?

When trying to find the inverse of the n$\times$n matrix $A$, one way of going about it is by solving $AX=I$, wherein $I$ is the n$\times$n identity matrix, and $X$ is some n$\times$n matrix which is ...
2
votes
4answers
41 views

Why do the addition of linear equations all pass through the same point

So I'm doing linear algebra right now and I have a question regarding addition of equations as part of Gauss' elimination algorithm. I understand why it's possible, as the LHS of one equation can be ...
2
votes
1answer
56 views

Is it possible for a system of equations to have a non-zero determinant and no solution at the same time?

I am quite confused by the solution I was given for the following problems: a) Solve the following system of equations using Gauss elimination only: $2x - y = 5$ $-x + 2y = -4$ $3x - y = -1$ b) ...
0
votes
1answer
27 views

Row reducing a matrix with determined pivots through Gauss-Jordan

In Algebra we've been given this matrix: $P=\begin{pmatrix} 3 & 2 & 6 & 10 \\ 8 & 4 & 9 & 5 \\ 7 & 3 & 12 & 4 \end{pmatrix}$ I'm asked to row-reduce it with ...
0
votes
1answer
40 views

solve linear system using gaussian elimination

I want to solve a linear system of the form Ax=b. First of all I create the augmented matrix (A|b). I apply some elementary row operations and i obtain the REF form of A. After than, I do not know ...
0
votes
2answers
32 views

finding determinant for matrix using upper triangle method!

so Here an example for matrix that I'm trying to evaluate its determinant! | 1 3 2 1| | 0 1 4 -4| | 2 5 -2 9| | 3 7 0 1| when applying first row operation i get | 1 3 2 1| | 0 1 ...
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0answers
26 views

Growth factor for Gaussian Elimination WITHOUT partial pivoting

A = $\begin{bmatrix} 1 & 7 & -11 \\ 4 & 29 & -50 \\ 6 & 49 & -107 \end{bmatrix}$ , after computing the LU factorization without partial pivoting I have L = ...
2
votes
2answers
38 views

Finding the inverse of a matrix by Gaussian elimination

I spent last hours trying to figure out how to solve the inverse matrix to this matrix: $$\begin{pmatrix} 2 &-3 & 1 \\ 1 & 2 &-1 \\ 2 & 1 & 1 \end{pmatrix}$$ The correct ...
0
votes
0answers
21 views

What changes where made on this Gaussian-Elimination?

in the Internet I have found the following use of the Gaussian Elimination method: $z \in \mathbb{R}, \ n\in\mathbb{N}, n \ge 2$ and $\begin{pmatrix} z & 1 & \dots & 1 & 1 \\ 1 & ...
1
vote
1answer
35 views

What is the canonical basis of a dualspace in $\mathbb{R}^3$?

I have the following: Consider the basis $$B := \{\begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, \begin{pmatrix} -1 \\ 1 \\ 2 \end{pmatrix}, \begin{pmatrix} 2 \\ 2 \\ 1 \end{pmatrix} \}$$ of the ...
1
vote
2answers
17 views

$3$ lines $4$ variables linear equation gaussian

So I'm currently taking a Linear Algebra class and am stuck on a problem. I have the equations: $$\begin{cases}\begin{align}&x + 2y - z + 3t = 3\\ &2x + 4y + 4z + 3t = 9\\ &3x + 6y - z ...
1
vote
1answer
83 views

Gauss-Jordan: Effect of column pivoting on result matrix

When I implement a Gauss-Jordan algorithm I can either have a 1 column result matrix or a multi-column result matrix (I mean the right hand side of the augmented matrix). The first case would be the ...
0
votes
1answer
59 views

Linear system of equations and multiple linear regression: Numerical solving

I am currently implementing a test procedure for data, namely a linear form of the Kramers-Kronig relations (paper here: http://jes.ecsdl.org/content/142/6/1885.abstract). This includes solving a ...
1
vote
1answer
112 views

Find the values of $k$ that make this system inconsistent, with unique solution, and with infinite solutions.

I've learned to find the solutions to linear systems using Gaussian Elimination. Moving on, I've found a new kind of exercise I hadn't done before: Find the values for $k$ that make this system: ...
0
votes
2answers
42 views

What did I do wrong with Gaussan Elimination for $\begin {cases} x + 5y + 11z = -5\\ 2x + 3y + 8z = 4\\ -x + 2y + 3z = -9 \end {cases}$?

Having problems with this one using Gaussian Elimination. Find the solutions for the linear equation system: $$\begin {cases} x + 5y + 11z = -5\\ 2x + 3y + 8z = 4\\ -x + 2y + 3z = -9 \end ...
3
votes
0answers
24 views

Row operations that change similarity class

Let $\mathbb{K}$ be a field and $A\in \mathcal{M}_{n\times n}(\mathbb{K})$ be a matrix. Which row operations on $A$ do not change its similarity class?
0
votes
1answer
23 views

Does non linear transform of Gaussain Random Variables results in Gaussian?

I have a question, if we do a non linear transformation on Gaussian random vector, will it give us Gaussian as a result? If No which techniques can we use to make sure the result is finally gaussian. ...
0
votes
5answers
45 views

How to solve this homogeneous system, with a missing column?

Find the solution set of triplets $(x,y,z)$ that fulfil this system using Gauss-Jordan: $$\begin {cases} -x + 2z = 0\\ 3x - 6z = 0\\2x - 4z = 0\end {cases}$$ First of all, I don't see any ...
1
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0answers
38 views

Using Gauss-Jordan for an infinite-solutions system

I'm starting to get the hang of this Gauss-Jordan stuff - well, I have never done a system with infinite solutions, so I decided to try this one. You can scroll to the bottom instead to see my doubts ...
1
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4answers
68 views

Are there no solutions for $\begin {cases} 2x+4y = 6\\ 3x+6y = 5\end {cases}$?

I'm trying to solve an equation system using Gauss-Jordan. $$\begin {cases} 2x+4y = 6\\ 3x+6y = 5\end {cases}$$ So, first, the augmented matrix: \begin{bmatrix} 2&4&5\\ 3&6&6\\ ...
2
votes
1answer
73 views

Can all equation systems be reduced to the identity matrix?

I'm trying to learn about solving equation systems using the Gauss-Jordan method. So, you have to convert the equation system to a matrix, and then reduce it to the identity. When you transform it to ...
1
vote
2answers
39 views

Row reduced matrix $\Leftrightarrow$ vectors (rows) are linearly independent.

Let $A$, a row-reduced matrix (after applying Gaussian elimination). Show that all rows which are different from $V_0$ (zero vector), are linearly independent. We learned this as sort of an ...
-2
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1answer
45 views

Finding the number of solutions to two equations

I have a question: For the following system of linear equations, using Gaussian elimination, decide whether it has at least one solution. If it does, represent the general solution as an affine map ...
-1
votes
2answers
51 views

Gauss Jordan Elimination [closed]

Apply Gauss-Jordan elimination to the following system and determine the general solution if it exists. $x+y+2z+3u+4v=0\\2x+2y+7z+11u+14v=0\\3x+3y+6z+10u+15v=0.$
0
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2answers
84 views

Gauss Elimination - Diagonal dominant matrices don't need row changes

I was asked to prove the following statement: let $A$ be an $n$ by $n$ matrix with real entries such that $\forall k \in \mathbb N, k\leq n$: $$\sum_{i \neq k} |A_{i,k}| < |A_{kk}|$$ Show that if ...
3
votes
1answer
66 views

LU factorization problem - Writing a code, don't understand partial pivoting

I'm trying to write a matlab code for the following question: The program gets a matrix $A$ (lets say square matrix) and it returns $P,L,U$ such that $PA=PLU$ and $P$ is the permutation matrix, the ...