Understanding Gaussian Elimination Matrices for Solving Linear Equations

[Samuelb88]

Homework Statement

What is the Gaussian elimination matrix for the vector for the vector $v=(2,-10,16,2)$?

The Attempt at a Solution

I don't understand the question. What is a "Gaussian elimination matrix for a vector?" I know that Gaussian elimination is a method for solving a system of linear equations, but I'm not sure what is meant/how to find the Gaussian elimination matrix, given a vector. Can someone please explain this to me?

Thanks

 

[Mark44]

Homework Statement

What is the Gaussian elimination matrix for the vector for the vector $v=(2,-10,16,2)$?

The Attempt at a Solution

I don't understand the question. What is a "Gaussian elimination matrix for a vector?" I know that Gaussian elimination is a method for solving a system of linear equations, but I'm not sure what is meant/how to find the Gaussian elimination matrix, given a vector. Can someone please explain this to me?

Thanks

I'll take a stab at it, since no one else has replied.

$$\begin{bmatrix} 1 & 0 & 0 & 0 & | & 2 \\ 0 & 1 & 0 & 0 & | & -10 \\ 0 & 0 & 1 & 0 & | & 16 \\ 0 & 0 & 0 & 1 & | & 2 \end{bmatrix}$$

What I'm showing here is a row-reduced augmented matrix that represents a system, for which the solution is the vector <2, -10, 16, 2>.

 

[Ray Vickson]

Homework Statement

What is the Gaussian elimination matrix for the vector for the vector $v=(2,-10,16,2)$?

The Attempt at a Solution

I don't understand the question. What is a "Gaussian elimination matrix for a vector?" I know that Gaussian elimination is a method for solving a system of linear equations, but I'm not sure what is meant/how to find the Gaussian elimination matrix, given a vector. Can someone please explain this to me?

Thanks

My guess would be that if you regard v as a _column_ vector they want you to determine the matrix E such that Ev becomes a simple unit vector, such as (1,0,0,0)^T,or maybe (2,0,0,0)^T. After all, that is how Gaussian elimination works: we determine linear combinations of rows such that a column is simplified; row operations = multiplication on the left by a matrix. (Or, maybe they want v to be a row vector, just as written, in which case they want a matrix E such that vE = something simple, like (2,0,0,0).)

RGV

 

[Samuelb88]

Thanks for the replies guys but I've solved this problem. In case you were wondering, I needed to find a matrix such that the image of the vector (2,-10,16,2) is the vector (2,-10,16,0). Pretty simple, I was just confused as to what exactly a "gaussian elimination matrix" was.

 

[Mark44]

In case you were wondering, I needed to find a matrix such that the image of the vector (2,-10,16,2) is the vector (2,-10,16,0).

This is this question you should have asked.

Pretty simple, I was just confused as to what exactly a "gaussian elimination matrix" was.