Question

Linear Algebra

\text { Let } A=\left[\begin{array}{ccc} 2 & 5 & 4 \\ 1 & 2 & -1 \\ -1 & -1 & 7 \end{array}\right] \text { and let } b=\left[\begin{array}{l} b_{1} \\ b_{2} \\ b_{3} \end{array}\right] . \text { Determine if the equation } A x=b \text { has a solution for any }

b in R3; if not find an equation for the span of the columns of A.