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

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2
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1answer
38 views

How was step 1 done in Gaussian Elimination?

Suppose I have matrix $B:= \begin{bmatrix}4 & -2 & 2\\-2 & 5 & 3\\ 2 & 3 & 7 \end{bmatrix} $ Performing Gaussian Elimination we get: EDIT corrected mistake. I mistakenly ...
0
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0answers
24 views

Find a basis for the span of each set?

I found the span of the set. Then I used GJ to get the RREF, and used the row reduced rows to form the basis. I got the basis as <( 1 0 -2 ; 0 1 1 )> However, my lecturer went a different way, ...
0
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2answers
17 views

Find the solution of binary xor operator equation

I am working in binary xor operator $\mathbb Z_2$. I have to resolve my problem such as $$\begin {cases} x_1+x_2+x_3=1\\ x_1+x_2=0\\ x_1+x_3=1\\ \end {cases}$$ Could you suggest to me any method to ...
0
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0answers
24 views

Quadratic Sieve, matrix problem

I read this: Quadratic Sieve Matrix Reduction and I am basically stuck. My Gaussian elimination says the answer is v= 0,0,0. Although you can clearly see that the correct answer is (1,1,1). How does ...
1
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2answers
30 views

Solving a system of equations with less equations than variables

For my discrete math/linear algebra class, one of our homework problems reads as follows: ...
1
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0answers
23 views

How to find the basis of a matrix by using Gauss-Elliminaton?

I confuse that, This is my calculating process, Where i do the mistake in this process? I hope to understand this error.
0
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1answer
23 views

What is the computational cost of reduced row echelon and finding the null space?

I'm taking computational linear algebra, and haven't been able to find too much information about the computational cost (in terms of m=rows and n=cols) of these two routines: Reduced Row Echelon ...
1
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1answer
40 views

Simple Eigenvalue finding question (by gauss elimination)

I saw a method for finding eigenvalues by using Gauss elimination to find an upper triangular matrix, then just taking the diagonal elements as the eigenvalues. It seems to work except for this case: ...
0
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1answer
27 views

finding the inverse of a matrx

In order to decrypt a cipher text using hill cipher, we must first find the inverse matrix of a given matrix. From this link http://en.wikipedia.org/wiki/Hill_cipher, ...
0
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2answers
17 views

How to solve this using gauss jordan method?

I am trying to solve the following equation using gauss jordan method but unable to solve due to the type of equations.At the end i am getting unwanted zeros in 2nd and 3rd row.Here is my work... ...
0
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0answers
22 views

Solve the following system using Gauss-Jordan elimination

$4x - 8y = 12$ $3x - 6y = 9$ $-2x + 4y = -6$ So the augmented matrix will be: $$ \begin{bmatrix} 4 && -8 && 12\\ 3&& -6 && 9\\ -2 && 4 && -6 ...
0
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1answer
28 views

Is it possible to solve pde with 2 Neumann boundary conditions (Gaussian Elimination)?

I have the following equation: $$ \nabla^2u = f $$ over $\Omega: [0,10] \times [0,10]$ where boundary conditions: $$ \left\{ \begin{array}{ll} \frac{\partial u (0,y)}{\partial x} = 0 \\ ...
0
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2answers
32 views

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. $$2x+z=7$$ $$x+y=2$$ $$y-z=-2$$ ...
1
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3answers
41 views

Why solving a system of linear equation produces the intersection of the equation

1) $x+y=1$ 2) $-x+y=1$ Geometrically we can visualize the two lines will intersect at $x=0, y=1$. Consider this algebraic solution using Gaussian Elimination, . But why do they be reduced to the ...
1
vote
1answer
42 views

If we know nullspace of matrix, how to find reduced row echelon form of that matrix?

vectors u = [4 1 0 0] and v = [1 0 2 1] form a base of nullspace of matrix $$ A\in M_{5,4}(R) $$ Find a reduced row echelon form of Matrix A. Since $ n-r = dimN(A) $ we know we got two base ...
1
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1answer
43 views

Binary Gaussian Elimination of a matrix

Can anyone help me find the algorithm for the Binary Gaussian elimination of a matrix. for example: The output:
0
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1answer
49 views

Solve the linear system by Gauss - Jordan elimination

$$ \begin{align} x& - y + 2z - w &= -1\\ 2x& + y - 2z - 2w &= -2\\ -x& + 2y - 4z + w &= 1\\ 3x& -3w &= -3 \end{align} $$ ...
0
votes
1answer
46 views

Solve the linear system by Gaussian elimination

$\begin{cases}-2b+3c=1 \\ 3a+6b-3c=-2 \\ 6a+6b+3c=5\end{cases}$ I got an inconsistent linear system with the third row being 0 0 0 6. May someone please verify if I am right? I looked it over.
0
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1answer
38 views

Matrix that needs to be reduced to reduced row echelon form

What does the first column mean? Do I move the first column to the last column?
0
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1answer
53 views

How to find system of equations from solution space

I have to find homogeneous system of linear equations whose solution space is: V = span((1,-2,4,3),(1,-1,6,4),(3,-8,8,3)). First I found vectors were linearly dependent, so I discarded the third ...
0
votes
1answer
57 views

Find solutions to magic puzzle with sums

I need help to solve the folowing puzzle using linear algebra (matrix and Gauss-Jordan Method): (for example the second horinzontal line: w + w + w + z = 45 or the ...
1
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1answer
63 views

Why must $b=0$ for this linear system to have infinitely many solutions for all $a$?

Consider the parameterized linear system of equations represented by the augmented matrix: $$ \left[ \begin{array}{ccc|c} 1 & 0 & a & 1 \\ 0 & 1 & 2 & 2 \\ 0 & 0 & ...
1
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1answer
43 views

Getting matrix in row echelon form - what's my error?

I start with $\begin{bmatrix} 1 & 2k & 1 & 0 \\ 0 & 1-6k & k-3 & 2 \\ 0 & 7k & 4 & 2 \end{bmatrix}$ I want to get it in row echelon form, so I'm looking for a ...
1
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1answer
25 views

Working with zeroes in Gaussian elimination

I am trying to find the null space of a matrix mod 2. So far I have tried to implement basic Gaussian elimination. Something happened that should've been very easy to solve but it's late and I can't ...
0
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1answer
29 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
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1answer
41 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
36 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
52 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
58 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
95 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
61 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
47 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
24 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
54 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
vote
2answers
706 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
votes
1answer
32 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: ...
0
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1answer
24 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
27 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
42 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
327 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
38 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
votes
1answer
39 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
votes
1answer
27 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
vote
1answer
33 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
279 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
vote
2answers
27 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
22 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
75 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
42 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
64 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) ...