1. Systems of linear equations. (a) For each of the following systems of linear equations, (1) solve it by putting the matrix in reduced row echelon form; (ii) for each of the consistent systems, identify the basic and free variables; (iii) determine the rank of the coefcient matrix. i. m+y+22=8 mZy+3z:1 3x7y+4z=10 x+2y+3z=1 y+2z=1 2x+y=5 iii. v+4:ny=1 2uv+5y4z=2 u+2m3y+2z=3 (b) 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) nd all the solutions. 3xy+sz=1 m+3y+22=t m2y+22=4 (c) 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) nd all the solutions. m+y=2 x+kz=1 2x+ky+82=0