# 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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### Is vector in the span?

So, from my understanding, a span is simply the space that can be made up of specified vectors. So if I wanted to find if vector $(1,2,3,4,5)$ was in the span of some vectors, I assume I should use ...
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1 vote
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### Determine rank of $A = \begin{bmatrix} 2 & 1 & -2 & 1 \\ 4 & 1 & -2 & -3 \\ 1 & -1 & 2 & -3 \\ 2 & 2 & -4 & -5 \\ 3 & 1 & -2 & 2 \end{bmatrix}$

Could you give me your feedback ? I've verified with https://matrix.reshish.com/rankCalculation.php but maybe there are things that could be done differently Determine the rank of the following ...
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### Traffic density of road network using System of Equations, Matrices and Gaussian Elimination

Could you give me your feedback ? We consider the following road system with the four intersections $A, B, C, D$. The numbers and variables correspond to the traffic density (Number of vehicles per ...
• 103
1 vote
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### Under which conditions is the following linear equation system solvable $x_1 + 2x_2 - 3x_3 = a$ $3x_1 - x_2 + 2x_3 = b$ $x_1 - 5x_2 + 8x_3 = c$

I'm unsure about the problem below Under which conditions is the following linear equation system solvable ? $$x_1 + 2x_2 - 3x_3 = a$$ $$3x_1 - x_2 + 2x_3 = b$$ $$x_1 - 5x_2 + 8x_3 = c$$ We set up ...
• 103
1 vote
43 views

### Determine inverse matrix of $A = \begin{bmatrix} 1 & 2 & -1 \\ -3 & 1 & 2 \\ -2 & 2 & 1 \end{bmatrix}$

Could you give me your feedback ? Determine the inverse of the following Matrix: $$A = \begin{bmatrix} 1 & 2 & -1 \\ -3 & 1 & 2 \\ -2 & 2 & 1 \end{bmatrix}$$ We want to ...
• 103
78 views

1 vote
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### Applications of the Gauss-Jordan elimination method

Aware of my minimal knowledge of linear algebra, I was seeing the power of the Gauss-Jordan elimination method. In particular, it can be used for: solve the linear systems $A\,X = b$; calculate the ...
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### Adding two terms in a Simultaneous Equation.

Sorry, but I have a problem where I must add two terms like this in a simultaneous equation: 2x + 4y = 32 2x - 3y = 11 I want to add the terms ...
28 views

### Problems with Simultaneous Equations

I have a problem with: 2x + 4y = 32 2x - 3y = 11 I know that I should add because the signs are different. But if I tried to eliminate the ...
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