Consider the system of linear equations:

2x + 4z = -2

-x + 2y - 3z = 4

x + 2y + z = k

Row- reduce the augmented matrix for the given system and then answer each of the following questions:

a) for what value(s) of k does the system of linear equations have a unique solution?

b) for what value(s) of k does the system of linear equations have no solution?

c) for what value(s) of k does the system of linear equations have infinitely many solutions?

d) for k where the system has infinitely many solutions, solve the system.

Where im having the most trouble is the row-reducing part. i was able to the x variables put in a way so that there was only 1 leading 1 in the column. however, im struggling ith the y and z. as well having the variable k there it is confusing me. please help if you can.