Question

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. 4x - y + 3z = 12, x + 4y + 6z = -32, 5x + 3y + 9z = 20, A.(8, -7, -2), B.(-8, -7, 9), C.none exist, D.(2, -7, -1).

Answer 1

Please help need serious math help

Answer 2

$$
A=\begin{bmatrix}
4 &-1 &3 &| &12 \\
1& 4 &6 &| &-32 \\
5 &3 & 9 &| &20
\end{bmatrix}
\\
\\
row(1)= -4*row(2)+row(1)\\
row(3)=-5+row(2)+row(3)\\


\rightarrow

\begin{bmatrix}
0 &-17 &-21 &| &140 \\
1& 4 &6 &| &-32 \\
0 &-17 & -21 &| &180
\end{bmatrix}
\\
row(1)=-row(3)+row(1)\\

\rightarrow

\begin{bmatrix}
0 &0 &0 &| &-40 \\
1& 4 &6 &| &-32 \\
0 &-17 & -21 &| &180
\end{bmatrix}
\\
\text{The 1st row means:}\\
0x+0y+0z=-40\\
\text{There is no way that any x,y,z can produce -40. There are no solutions}
$$