Question

Which of the following can not be used on a matrix when solving a system of equations? interchange rows multiply a row by a constant add a constant to a row

Answer 1

The third one

Answer 2

Example:
\[(1)\begin{cases}x+y=1\\
x-y=2\end{cases}\]
Interchanging the rows gives an identical system:
\[\begin{cases}x-y=2\\
x+y=1\end{cases}\]
Multiplying a row by a constant doesn't fundamentally change the system; you can always undo that operation:
\[\begin{cases}2x+2y=2\\
x-y=2\end{cases}\]
Adding a constant to a row makes a completely new system:
\[(2)\begin{cases}x+y=2\\
x-y=2\end{cases}\]
System (1) has solution \(x=\dfrac{3}{2},y=-\dfrac{1}{2}\) whereas system (2) has solution \(x=2,y=0\).