Mathematics, 08.04.2020 03:12, Kurlyash
Solve the given system of equations by either Gaussian elimination or Gauss-Jordan elimination. (If the system is inconsistent, enter INCONSISTENT. If the system is dependent, express x, y, and z in terms of the parameter t.) 5x − 2y + 4z = 12 x + y + z = 8 4x − 3y + 3z = 4 (x, y, z) = 2(−3z+14) 7, −z+28 7,t
Answers: 3
![\left[\begin{array}{ccc}5&-2&4 :12\\1&1&1 : 8\\4&-3&3 : 4\end{array}\right]\to\left[\begin{array}{ccc}1&1&1 :8\\5&-2&4 : 12\\4&-3&3 : 4\end{array}\right] (R_1\iff R_2)\\\implies \left[\begin{array}{ccc}1&1& 1:8\\0&-7&-1 : -28\\0&-7&-1 : -28\end{array}\right] (R_{2}^{'}=R_2-5R_1,R_{3}^{'}=R_3-4R_1)\\\implies \left[\begin{array}{ccc}1&1&1 :8\\0&-7&-1 :-28\\0&0&0 : 0\end{array}\right] (R_{3}^{'}=R_3+R_2)\\\implies \left[\begin{array}{ccc}1&1&1 :8\\0&1&1/7 : 4\\0&0&0 : 0\end{array}\right]](/tpl/images/0588/7362/5f8fd.png)
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