# Questions tagged [gaussian-elimination]

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

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### Gauss-Jordan elimination gives inconsistent matrix for a consistent system?

I am trying to get an analytical expression for a steady state of an ODE system governing a chemical reaction network via symbolic computer algebra systems. As an example for this question I'll take a ...
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### Convert any non-singular square matrix to a strictly diagonally dominant one using only elementary row operations

Elementary row operations Swap the positions of two of the rows. Multiply one of the rows by a nonzero scalar. Add or subtract the scalar multiple of one row to another row. Strictly diagonally ...
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### Gaussian Elimination when Order of Operations Matters

I've been self studying linear algebra and was hoping that someone could provide some insight and/or direct me to the right resource here. Let's say that we are playing the game lights out. Math.SE ...
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### How to solve nonlinear system of equations with Gaussian and Seidel?

For one of our college projects we’re required to solve numerous vector loops that get bigger and bigger. We weren’t quite taught Gaussian elimination and the Seidal iterative method but our lecturer ...
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### Determine the base and the dimension of subspace $W$ given as generated space (set of linear combinations) of $3$-vectors in $\mathbb{R}^4$

Hello everybody I'm not certain with this question. So if lets say $$W = L\bigl((1,1,0,-1),\, (0,-1,1,1),\, (3,1,2,-1)\bigr) \subset \mathbb{R}^4;$$ $L$ being the space generated or set of linear ...
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### Can you use row operations to reduce a matrix to either upper or lower triangular to find the eigenvalues?

For example, we have the matrix $$\begin{bmatrix}-1&0&1\\2&6&-14\\1&0&-1 \end{bmatrix}$$ Using row operations $R_3+R_1$ and $R_2 + 2R_1$ and finally $-1R_1$, we arrive at \...
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### Growth of a completely pivoted Matrix

Let A be a CP matrix.( A completely pivoted matrix is one such that during the Gauss transformation with full pivoting there is no need to exchange rows or columns) We apply to it Gaussian elimination....
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### How can I do Gaussian elimination of a $32 \times 32$ bit matrix?

I have been looking at how to reverse the sigma operation in the sha256 hash and in several places I have seen that you have to make a $32 \times 32$ bit matrix and then solve it with Gaussian ...
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### How to efficiently find this special case zero-eigenvector?

I have a real 3x3 symmetric matrix. I know that its 3 eigenvalues are 0 (within precision) and two real numbers >>0. What's the most efficient way to find the eigenvector corresponding to the ...
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### How does the Gaussian elimination method work to find the inverse matrix

How does augmenting a square matrix (LHS) with an identity matrix (RHS) and then reducing the square matrix to an identity matrix and performing the same operations on the identity matrix using ...
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### Formula for last element of zero row in symbolic gaussian elimination without swapping any rows

Suppose we have an overdetermined matrix with $n$ rows and $n-1$ columns. We augment it with a column-matrix and then do Gaussian elimination on the augmented matrix. Assume that no row swapping is ...
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Suppose that we are operating in a three-digit decimal floating point system. We want to use Gaussian Elimination with Partial Pivoting (GEPP) to find the inverse of a given invertible $2\times2$ ...