Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.3x + 5y - 2w = -132x + 7z - w = -14y + 3z + 3w = 1-x + 2y + 4z = -5A. {(-1, -1 , 0, )}B. {(1, -2, 0, 3)}C. {( , -2, 0, )}D. {( , - , 0, )}

Answer with explanation:The given system of equation are      3x + 5y - 2w = -13    2x + 7z - w = -1  4y + 3z + 3w = 1 -x + 2y + 4z = -5Writing the system of equation in terms of Augmented Matrix   [tex]\left[\begin{array}{ccccc}3&5&0&-2&-13\\2&0&7&-1&-1\\0&4&3&3&1\\-1&2&4&0&-5\end{array}\right]\\\\R_{3} \leftrightarrow R_{4}\\\\\left[\begin{array}{ccccc}3&5&0&-2&-13\\2&0&7&-1&-1\\-1&2&4&0&-5\\0&4&3&3&1\end{array}\right]\\\\R_{3} \rightarrow 2R_{3}+R_{2}\\\\\left[\begin{array}{ccccc}3&5&0&-2&-13\\2&0&7&-1&-1\\0&4&15&-1&-11\\0&4&3&3&1\end{array}\right]\\\\R_{4}\rightarrow R_{4}-R_{3}\\\\\left[\begin{array}{ccccc}3&5&0&-2&-13\\2&0&7&-1&-1\\0&4&15&-1&-11\\0&0&-12&4&12\end{array}\right][/tex] [tex]R_{2}\rightarrow 3R_{2}-2R_{1}\\\\\left[\begin{array}{ccccc}3&5&0&-2&-13\\0&-10&21&1&23\\0&4&15&-1&-11\\0&0&-12&4&12\end{array}\right]\\\\R_{3}\rightarrow 5R_{3}+2R_{2}\\\\\left[\begin{array}{ccccc}3&5&0&-2&-13\\0&-10&21&1&23\\0&0&117&-3&-9\\0&0&-12&4&12\end{array}\right]\\\\ R_{4}\rightarrow 3R_{4}+4R_{3}\\\\\left[\begin{array}{ccccc}3&5&0&-2&-13\\0&-10&21&1&23\\0&0&117&-3&-9\\0&0&432&0&0\end{array}\right][/tex]→432 z=0z=0⇒117 z-3 w=-9-3 w=-9Dividing both sides by -3w=3⇒-10 y+21z+w=23-10 y+0+3=23-10 y=23-3-10 y= 20y=-2⇒3 x+5 y-2w=-133 x+5 ×(-2)-2 ×3= -133 x-10-6= -133 x=16-133 x=3x=1Option B. {(1, -2, 0, 3)}