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
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 ...
1
vote
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 ...
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
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
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) ...
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
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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
113 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 ...
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
vote
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
1answer
60 views

Prove Gaussian Elimination Preserves this Matrix Property

Prove or disprove that if a matrix has the property $0 \neq |a_{ii}| \leq \sum_{\substack{j=1 \\j \neq i }}|a_{ij}|$ Then Gaussian elimination without pivoting will preserve this property I have ...
2
votes
1answer
201 views

Gauss-Jordan Elimination to solve for variables

I have the following linear system: $$x + 2y - 3z = 4$$ $$3x - y + 5z = 2$$ $$4x + y + (s^2 - 14)z = s+2$$ Im trying to solve for $s$ to figure out how many solutions it has (if any). I know how to ...