# 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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### Conjecture with a three-diagonal system of equations

Everything in the sequel real-valued. And it is silently assumed that the denominators are non-zero, though the latter is not a trivial issue. Consider a piece of an (infinitely) large system of ...
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### Why does Gaussian elimination for band matrices take $\omega$ operations to eliminate the first element?

I am currently reading through G. Strang’s “Linear Algebra and its applications” and there is this chapter about band and symmetric matrices which just does not stop confusing me. In this case we have ...
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### Writing a vector a a sum of two vectors

Write $\mathbf u =\begin{bmatrix}9\\-1\\2\end{bmatrix}$ as a sum of two vectors where one is orthogonal to the plane $x+2y-2z=0$ and the other is parallel to the same plane. I've attempted to use ...
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### How would I convert this matrix to a system of equations?

Given a matrix $$A =\begin{pmatrix}1& 1& 1\\−2& 1& 3\\3& 2& 1\end{pmatrix}$$ use Gaussian elimination to compute the determinant $\det(A)$ of $A$ and to solve the system of ...
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### Solving a linear equation system in $\mathbb{Z}_q$, where $q$ prime

I am wondering about the following: Assume you have a linear equation system of the form: $$Ax = b$$, where $A \in \mathbb{Z}_q^{n \times m}$, $x \in \mathbb{Z}_q^m$, $b \in \mathbb{Z}_q^n$ and we ...
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### How to solve a system of 32 XOR equations via Gaussian Elimination?

In the beginning, I needed to solve a system of linear XOR equations. I was inspired by the answer to this question: how to solve system of linear equations of XOR operation? , and started solving my ...