7.6 Solving systems with gaussian elimination  (Page 5/13)

Can any system of linear equations be written as an augmented matrix? Explain why or why not. Explain how to write that augmented matrix.

Can any matrix be written as a system of linear equations? Explain why or why not. Explain how to write that system of equations.

Is there only one correct method of using row operations on a matrix? Try to explain two different row operations possible to solve the augmented matrix $\left[\begin{array}{rr}\hfill 9& \hfill 3\\ \hfill 1& \hfill -2\end{array}|\begin{array}{r}\hfill 0\\ \hfill 6\end{array}\right].$

Can a matrix whose entry is 0 on the diagonal be solved? Explain why or why not. What would you do to remedy the situation?

Can a matrix that has 0 entries for an entire row have one solution? Explain why or why not.

$\begin{array}{l}8x\mathrm{-37}y=8\\ 2x+12y=3\end{array}$

$\begin{array}{l}16y=4\hfill \\ 9x-y=2\hfill \end{array}$

$\begin{array}{l}3x+2y+10z=3\hfill \\ \mathrm{-6}x+2y+5z=13\hfill \\ 4x+z=18\hfill \end{array}$

$\begin{array}{l}\hfill \\ x+5y+8z=19\hfill \\ 12x+3y=4\hfill \\ 3x+4y+9z=\mathrm{-7}\hfill \end{array}$

$\begin{array}{l}6x+12y+16z=4\hfill \\ 19x\mathrm{-5}y+3z=\mathrm{-9}\hfill \\ x+2y=\mathrm{-8}\hfill \end{array}$

$\left[\begin{array}{rr}\hfill \mathrm{-2}& \hfill 5\\ \hfill 6& \hfill \mathrm{-18}\end{array}|\begin{array}{r}\hfill 5\\ \hfill 26\end{array}\right]$