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

a) k=1, h=1, 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=3 the system has no solutions.

Step-by-step explanation:

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=1 and h=1, 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=3, the system has no solutions because the last equation of the system of the echelon form of the matrix is

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.