Math  /  Algebra

QuestionSolve the system of equations using matrices. Use the Gaussian elimination method with back-substitution. {2x+3y+4z=295x5y2z=13x2y=6\left\{\begin{array}{rr} 2 x+3 y+4 z & =-29 \\ 5 x-5 y-2 z & =-13 \\ x-2 y & =-6 \end{array}\right.
Use the Gaussian elimination method to obtain the matrix in row-echelon form. Choose the correct answer below. A. [160201251750016]\left[\begin{array}{rrr|c}1 & -6 & 0 & -2 \\ 0 & 1 & -\frac{2}{5} & \frac{17}{5} \\ 0 & 0 & 1 & -6\end{array}\right] B. [102601251750016]\left[\begin{array}{rrr|c}1 & 0 & -2 & -6 \\ 0 & 1 & -\frac{2}{5} & \frac{17}{5} \\ 0 & 0 & 1 & -6\end{array}\right] C. [120601175250016]\left[\begin{array}{rrr|r}1 & -2 & 0 & -6 \\ 0 & 1 & \frac{17}{5} & -\frac{2}{5} \\ 0 & 0 & 1 & -6\end{array}\right] D. [120601251750016]\left[\begin{array}{rrr|c}1 & -2 & 0 & -6 \\ 0 & 1 & -\frac{2}{5} & \frac{17}{5} \\ 0 & 0 & 1 & -6\end{array}\right]

Studdy Solution
Identify the correct row-echelon form from the given options:
The resulting row-echelon form is: [1026012435107350016]\left[\begin{array}{rrr|c} 1 & 0 & -2 & -6 \\ 0 & 1 & \frac{24}{35} & -\frac{107}{35} \\ 0 & 0 & 1 & -6 \end{array}\right]
This matches option B: [102601251750016]\left[\begin{array}{rrr|c} 1 & 0 & -2 & -6 \\ 0 & 1 & -\frac{2}{5} & \frac{17}{5} \\ 0 & 0 & 1 & -6 \end{array}\right]
The correct answer is option B.

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