Question

Convert the given system to an augmented matrix. 2x1 8x2 − 4x3 = −16 −x1 − 3x2 5x3 = 7

Answer 1

To convert a system of equations to an augmented matrix, the coefficients of the variables and the constants are placed into a matrix, with each equation represented by a row in the matrix.

Step-by-step explanation:

To convert the given system of equations to an augmented matrix, we will organize the coefficients of the variables and the constants into matrix form. The system of equations is:

1. 2x1 + 8x2 - 4x3 = -16
2. -x1 - 3x2 + 5x3 = 7

The corresponding augmented matrix is created by placing the coefficients of the variables x1, x2, and x3 in the first, second, and third columns, respectively, and the constants in the fourth column:

\[\begin{bmatrix}
2 & 8 & -4 & | & -16 \\
-1 & -3 & 5 & | & 7
\end{bmatrix}\]