Chose parameters h and k such that the system has a) a unique solution, b) many solutions, and c) no solution. 31+3x2= 4 2x1+kx2= h

Answer

a) k=7, h=9, the unique solution of the system is  

b) If k=6 and h=8 the system has infinite solutions.

c)If k=6 and h=9 the system has no solutions.

Step-by-step explanation:

I am assuming that the system is x1+3x2=4; 2x1+kx2=h

The augmented matrix of the system is . If two times the row 1 is subtracted to row 2 we get the following matrix.

Then

a) If k=7 and h=9, the unique solution of the system is and solviong for ,

Then the solution is

b) If k=6 and h=8 the system has infinite solutions because the echelon form of the matrix has a free variable.

c)If k=6 and h=9 the system has no solutions because the last equation of the system of the echelon form of the matrix is