Question

X+2y+3z=8

x+y-z=2
2x+y+z=5

With Gaussian Elimination, write down the augmented matrix associated with the system, just the matrix, without proceeding to solve it for this part.

Answer 1

The augmented matrix for the system using Gaussian Elimination is represented as [[1, 2, 3, 8], [1, 1, -1, 2], [2, 1, 1, 5]].

Step-by-step explanation:

The augmented matrix associated with the system of equations provided can be written without proceeding to solve it. This is part of the first steps in Gaussian Elimination, a method of solving systems of linear equations. The given system:

• x + 2y + 3z = 8
• x + y - z = 2
• 2x + y + z = 5

can be represented as the following augmented matrix:

\[\begin{pmatrix}
1 & 2 & 3 & | & 8 \\
1 & 1 & -1 & | & 2 \\
2 & 1 & 1 & | & 5
\end{pmatrix}\]

This matrix contains the coefficients of the variables in the three equations as well as the constants on the right side of the equality.