1. Discuss each of the three operations in Gaussian elimination. What do they have in common and how do they help solve systems of linear equations?
2. What is an Eigenvalue? What is an Eigenvector?

Suppose you need to find numbers x, y, and z such that the following three equations are all simultaneously true:
2x + y − z = 8,
− 3x − y + 2z = − 11,
− 2x + y + 2z = − 3
This is called a system of linear equations for the unknowns x, y, and z. They are called linear because each term is either constant or is a constant times a single variable to the first power. The goal is to transform this system to an equivalent one so that we can easily read off the solution. The operations to transform a system of equations to another, whilst still preserving the solutions are as follows:
? multiply or divide a row by a non-zero number
? switch two rows
? add or subtract a (not necessarily integer) multiple of one row to another one
The strategy is as follows: eliminate x from all but the first equation, eliminate y from all but the second equation, and then ...

Solution Summary

The solution provides detailed theory for the problem in a 3-page Word document.

Please find the question attached to the document below.
function [x] = gaussel(A,b)
% [x] = gaussel(A,b)
%
% This subroutine will perform Gaussianelimination
% and back substitution to solve the system Ax = b.
% INPUT : A - matrix for the left hand side.
% b - vector for the right hand side
%
% OUTPUT : x -

QUESTION:
Solve the system of equations by the Gaussianelimination method.
2x + y –3z =1
3x - y + 4z =6
x + 2y - z =9
My response: Please explain if I am wrong. I have several more to do.
2 1 -3 1
3 -1 4 6
1 2 -1 9

Please help with solving the following question regarding Gaussian eliminations to a system.
The system
[see the attachment for the matrix and equation]
Where a_ij = 0 whenever i-j >= 2
Do an operation count of MD (Multiplications/Division) and AS (Addition/Subtraction) when using Gaussianelimination to solve the syst

Solve the following linear system using Gaussianelimination.
Show work.
2y + z = 4
x+ y +z = 6
2x + y + z = 7
Solve the following linear system for x using Cramer's rule.
Show work.
4x - y + z = -5
2x + 2y + 3z = 10
5x - 2y + 6z = 1

Matrices are the most common and popular way to solve systems of equations.
Provide an example of a matrix that can be solved using Gaussianelimination.
Show specifically how row operations can be used to solve the matrix.
State the solution.
Substitute the solution back into the equation to verify the solution.
O

1). Write the matrix in reduced row-echelon form: [1, 2, -1, 3], [7, -1, 0, 2], [3, 2, 1,-1].
2) Find the equation of the parabola that passes through the given points. Use the graphing utility to verify your result. (Please look at the picture).
3) Use a graphing utility to find AB, given. A= [1, 3, 6], [4, 1, 3] B= [0, 1

17. Solve the system of equations by the Gaussianelimination method.
x- 3y + z= 8
2x- 5y -3 z= 2
x + 4y + z= 1
18. Find the inverse of the given matrix.
1 2
-2 -3
19. Evaluate the determinant by expanding by cofactors.
-2 3 2
1 2 -3
-4 -2 1
20. Solve the system of

Matrices are the most common and popular way to solve systems of equations.
Provide an example of a matrix that can be solved using Gaussianelimination.
1. Show specifically how row operations can be used to solve the matrix.
2. State the solution
3. substitute the solution back into the equation to verify the solution.