(Solved): \( \operatorname{Let} A=\left[\begin{array}{rrr}1 & -2 & -1 \\ -3 & 3 & 0 \\ 4 & -2 & 2\end{array}\ ...

\( \operatorname{Let} A=\left[\begin{array}{rrr}1 & -2 & -1 \\ -3 & 3 & 0 \\ 4 & -2 & 2\end{array}\right] \) and \( b=\left[\begin{array}{c}b_{1} \\ b_{2} \\ b_{3}\end{array}\right] \) solution. Show that the equation \( A x=b \) does not have a solution for all possible \( b \), and describe the set of al \( b \) for wtich \( A x=b \) does have a How can it be shown that the equation \( A x=b \) does not have a solution for all possible b? Choose the correct answer below A. Find a vector \( x \) for which \( A \mathbf{x}=\mathrm{b} \) is the zero vector B. Row reduce the augmented matrix \( [\mathrm{A} \) b \( ] \) to demonstrate that \( [\mathrm{A} \quad \mathrm{b}] \) has a pivot position in every row. \( C \). Find a vector \( b \) for which the solution \( t o A x=b \) is the zero vector. D. Row reduce the matrix. A to demonstrate that \( A \) has a pivot position in every tow. Row reduce the matrix A to dernonstrate that A does not have a pivot position in every tow Describe the set of all \( b \) for which \( A x=b \) does have a soluticn. \( \mathrm{D}= \) (Typt an expressian using \( b_{1}, b_{2} \), and \( b_{3} \) as the variables and 1 as the coefficient of \( b_{3} \) )