Systems of Linear Equations

Find all values of s and t such that the following system of equations, (i) is inconsistent, (ii) is independent, (iii) is dependent. In case of (ii) and (iii) find all the solutions.

3x y + sz = 1

x + 3y + 2z = t

x 2y + 2z = 4

Find all values of k such that the following system of equations, (i) is inconsistent, (ii) is independent, (iii) is dependent. In case of (ii) and (iii) find all the solutions. x + y = 2

x + kz = 1

2x + ky + 8z = 0