Which matrix indicates that the equations of its associated system of equations has infinitely many solutions?
A) $\left[ \begin{array} { c c : c }
1 & - 9 & 5 \
0 & 1 & 1
\end{array} \right]$
B) $\left[ \begin{array} { c c : c }
1 & - 9 & 5 \
0 & 0 & 6
\end{array} \right]$
C) $\left[ \begin{array} { c c : c }
1 & - 2 & 3 \
0 & 0 & 0
\end{array} \right]$
D) $\left[ \begin{array} { l l : l }
1 & 0 & 5 \
0 & 1 & 1
\end{array} \right]$

Question

Which matrix indicates that the equations of its associated system of equations has infinitely many solutions?
A) $\left[ \begin{array} { c c : c } 
1 & - 9 & 5 \
0 & 1 & 1
\end{array} \right]$
B) $\left[ \begin{array} { c c : c } 
1 & - 9 & 5 \
0 & 0 & 6
\end{array} \right]$
C) $\left[ \begin{array} { c c : c } 
1 & - 2 & 3 \
0 & 0 & 0
\end{array} \right]$
D) $\left[ \begin{array} { l l : l } 
1 & 0 & 5 \
0 & 1 & 1
\end{array} \right]$

Quizplus · Accepted Answer

If a row reduces to have a row of all zeroes, except for the last column being a non-zero number, then the system of equations corresponding to the matrix will have infinitely many solutions. In this case, the second equation reduces to 0x + 0y = 0, which means that there are infinitely many solutions because it doesn't place any restrictions on x and y.

Which Matrix Indicates That the Equations of Its Associated System [1−95011]\left[ \begin{array} { c c : c } 1 & - 9 & 5 \\0 & 1 & 1\end{array} \right][10​−91​51​]

Which Matrix Indicates That the Equations of Its Associated System $\left[ \begin{array} { c c : c } 1 & - 9 & 5 \\0 & 1 & 1\end{array} \right]$