1. The problem statement, all variables and given/known data Choose h and k such that the system has a) no solution b) a unique solution and, c) many solutions. Give separate answers for each part. x1 + hx2=2 4x1+8x2=k 2. Relevant equations 3. The attempt at a solution I set up the matrix [1 h 2 ] [4 8 k ] and I multiplied the top row by -4 and added the 3rd row to it to get [ 1 ----- h ----- 2 ---] [ 0 (-4h+8) (-8+k) ] To get part A) -no solution-, I figured that the 2nd column cannot equal 0, therefore if h=2, and k does not equal 8, then there is no solution. Here is where I get lost... I didn't get these answers that the book says: For part B), unique solution, h does not equal 2....but what does that mean? If h doesn't equal 2 then that means it can take on any value besides 2, therefore k can be almost any value as well. For part C), many solutions, that books says h=2 and k=8 So that means for the 2nd row you would get 0=0....so wouldn't we just disregard that? then we are left with the 1st row saying 1(x1)+2(x2)=2 I don't understand parts B and C. Another question: Am I right to assume that we're just looking at -4h+8 here? Or should I also be considering -8+k?? Thanks!