Question

Find a solution to the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations

Answer 1

The following matrix when written in the form of Augmented Matrix

`\begin{bmatrix}4&-2&-5&-51\\4&-1&-2&-36\\4&-2&4&-24\end{bmatrix}\\\\R_(2)\to R_(2)- R_(1)\\\\ R_(3)\to R_(3)- R_(1)\\\\\begin{bmatrix}4&-2&-5&-51\\0&1&3&15\\0&0&9&27\end{bmatrix}\\\\R_(3)\to (R_(3))/(9)\\\\R_(2)\to R_(2)- 3R_(3)\\\\\begin{bmatrix}4&-2&-5&-51\\0&1&0&6\\0&0&  1&3\end{bmatrix}\\\\R_(1)\to R_(1)+2 R_(2)\\\\\begin{bmatrix}4&  0&-5&-39\\0&1&0&6\\0&0&1&3\end{bmatrix}\\\\\\\\R_(1)\to R_(1)+5 R_(3)`

`\begin{bmatrix}4&0&0&-24\\0& 1& 0& 6\\0& 0& 1& 3\end{bmatrix}\\\\R_(1)\to (R_(1))/(4)\\\\\begin{bmatrix} 1&0&0&-6\\0& 1& 0& 6\\0&0&1&3\end{bmatrix}\\\\x= -6, y=6,z=3`

Option A: x= -6,y=6 and z=3

Answer 2

Option A. (-6,6,3)

Explanation:

Please, see the attached file.

Thanks.