Let $A= \left[{\begin{matrix} 5 & 10 & 5 & 25 \cr 2 & 6 & 6 & 16 \cr 3 & 1 & -8 & -3 \cr 5 & 9 & 1 & 16 \cr \end{matrix}}\right]$, and ${\bf x}=\ \left[{\begin{matrix} x_1 \cr x_2 \cr x_3 \cr x_4 \cr \end{matrix}}\right]$.

We want to determine if $A{\bf x}={\bf b}$ has a unique solution for every ${\bf b}\in {\mathbb R}^4$.

Choose the best answer

A. The equation has a unique solution for every ${\bf b}\in {\mathbb R}^4$ because the number of rows and columns in $A$ is the same.
B. The equation does not have a unique solution for every ${\bf b}\in {\mathbb R}^4$ because after row reducing matrix $A$ we get a matrix with a row of zeros.
C. The equation has a unique solution for every ${\bf b}\in {\mathbb R}^4$ because after row reducing matrix $A$ we get a matrix with a row of zeros.
D. The equation does not have a unique solution for every ${\bf b}\in {\mathbb R}^4$ because after row reducing matrix $A$ we get a matrix without a row of zeros.
E. The equation has a unique solution for every ${\bf b}\in {\mathbb R}^4$ because after row reducing matrix $A$ we get a matrix without a row of zeros.
F. The equation does not have a unique solution for every ${\bf b}\in {\mathbb R}^4$ because the number of rows and columns in $A$ is the same.
G. We cannot tell if the equation has a unique solution for every ${\bf b}\in {\mathbb R}^4$.