Determine the number of solutions to the augmented matrix.
$\left[\begin{array}{rrrrr}
1 & 2 & 0 & 1 & 4 \
0 & 1 & -1 & -3 & 2 \
0 & 0 & 1 & 3 & 5 \
0 & 0 & 0 & 0 & 1
\end{array}\right]$
A) infinitely many
B) 2 solutions
C) 1 solution
D) no solutions

Question

Quizplus · Accepted Answer

The presence of a row in the augmented matrix where all the coefficients of the variables are 0 but the constant term is non-zero (in this case, the last row [0 0 0 0 1]) indicates that the system of equations is inconsistent. This means there are no solutions to the system.

Determine the Number of Solutions to the Augmented Matrix [1201401−1−320013500001]\left[\begin{array}{rrrrr}1 & 2 & 0 & 1 & 4 \\0 & 1 & -1 & -3 & 2 \\0 & 0 & 1 & 3 & 5 \\0 & 0 & 0 & 0 & 1\end{array}\right]​1000​2100​0−110​1−330​4251​​

Determine the Number of Solutions to the Augmented Matrix $\left[\begin{array}{rrrrr}1 & 2 & 0 & 1 & 4 \\0 & 1 & -1 & -3 & 2 \\0 & 0 & 1 & 3 & 5 \\0 & 0 & 0 & 0 & 1\end{array}\right]$