(Step-by-Step) a) For what vectors v=[la , b , c] does the equation A x=v have a solution if A= [ccc1 0 1 , 0 -1 2 , 1 -1 3], and x=[lx_1 , x_2 , x_3] b)
Question: a) For what vectors \(v=\left[\begin{array}{l}a \\ b \\ c\end{array}\right]\) does the equation \(A x=v\) have a solution if \(A=\)
\(\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & -1 & 2 \\ 1 & -1 & 3\end{array}\right]\), and \(x=\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_{3}\end{array}\right]\)
b) What is the rank of the matrix A
c) What is the dimension of \(\operatorname{im}(A)\) ? What is the dimension of \(\operatorname{ker}(A)\) ?
Deliverable: Word Document 
