$1\mathrm{.}1\mathrm{.}3.$ The system $2x=-6,-4x+3y=3,x+4y-z=7,$ is in lower triangular form. $($a$)$ Formulate a method of Forward Substitution to solve it$.($b$)$ What happens if you reduce the system to $($upper$)$ triangular form using the algorithm in this section?

$($c$)$ Devise an algorithm that uses our linear system operation to reduce a system to lower triangular form and then solve it by Forward Substitution.

$($d$)$ Check your algorithm by applying it to one or two of the systems in Exercise $1\mathrm{.}1\mathrm{.}1.$ Are you able to solve them in all cases?