Exercise $3.($CS$1\mathrm{.}2)$

Consider the following triangular system:

$x+y+z+w,=2$

$-6z+5w,=b_2$

$3z-w,=-1$

$2w,=-4$

where $b_2$ is a real number.

$3$

a$.$ For what value$($s$)$ of $b_2,$ if any at all, does this system have a unique solution? Briefly justify your answer with a short explanation or short calculation.

b$.$ For what value$($s$)$ of $b_2,$ if any at all, does this system have infinitely many solutions? Briefly justify your answer with a short explanation or short calculation.

c$.$ For what value$($s$)$ of $b_2,$ if any at all, does this system have no solution? There's no need to justify your answer to $($c$)$ as it will be the complement of your answers to $($a$)$ and $($b$).$