(i) For which value k will every system of linear equations with k equations and 5 variables have

infinitely many solutions?

Answer:

(ii) A certain homogeneous system of linear equations with 5 equations and 4 variables has a

unique solution. What is the rank of its augmented matrix?

Answer:

(iii) The rank of the augmented matrix of an inconsistent system of linear equations is 5. What

is the minimum number of unknowns the system may have?

Answer:

(iv) The solution of a system of linear equations with 8 variables can be expressed in a

parametric form with three parameters. What is the rank of the augmented matrix of the system?