Question 19
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Write the augmented matrix for the system of linear equations.
\[
\left\{\begin{array}{l}
-2 x+5 y+8 z=1 \\
3 x+6 y+2 z=27 \\
8 x+8 y+3 z=73
\end{array}\right.
\]
Select one:
a. $\left[\begin{array}{rrr|r}1 & -2 & 5 & 8 \\ 27 & 3 & 6 & 2 \\ 73 & 8 & 8 & 3\end{array}\right]$
b. $\left[\begin{array}{rrr|r}-2 & 8 & 8 & 1 \\ 5 & 6 & 8 & 27 \\ 8 & 2 & 3 & 73\end{array}\right]$
c. $\left[\begin{array}{rrr|r}1 & 8 & 5 & -2 \\ 27 & 2 & 6 & 3 \\ 73 & 3 & 8 & 8\end{array}\right]$
d. $\left[\begin{array}{rrr|r}-2 & 5 & 8 & 1 \\ 3 & 6 & 2 & 27 \\ 0 & 0 & -3 & 73\end{array}\right]$
Time left 1:08:08
Answer
Write the augmented matrix for the system of linear equations. The augmented matrix is formed by writing the coefficients of the variables and the constants from the right-hand side of the equations as the entries of the matrix. The coefficients of \(x\), \(y\), and \(z\) form the first, second, and third columns of the matrix, respectively, and the constants form the fourth column. Therefore, the augmented matrix for the given system of equations is \(\left[\begin{array}{rrr|r}-2 & 5 & 8 & 1 \ 3 & 6 & 2 & 27 \ 8 & 8 & 3 & 73\end{array}\right]\).
Step 1 ：Write the augmented matrix for the system of linear equations. The augmented matrix is formed by writing the coefficients of the variables and the constants from the right-hand side of the equations as the entries of the matrix. The coefficients of \(x\), \(y\), and \(z\) form the first, second, and third columns of the matrix, respectively, and the constants form the fourth column. Therefore, the augmented matrix for the given system of equations is \(\left[\begin{array}{rrr|r}-2 & 5 & 8 & 1 \ 3 & 6 & 2 & 27 \ 8 & 8 & 3 & 73\end{array}\right]\).
