# Thread: matrix solution and calculator input

1. ## matrix solution and calculator input

how can i state the following condition l^2 + m^2 + n^2 = 1 into the following matrix

[-56.8 -55 -75] [l] =0
[-55 -121.8 33] [m] =0
[-75 33 -261.8] [n] =0

2. If the determinant of that matrix is not 0, you can't- that matrix equation has a single solution which may or may not satisfy that additional condition. If the determinant is 0 (I haven't checked but I imagine that's why you are asking) then probably the best thing to do is to go ahead and "try" to solve the equation- since the determinant is 0, you won't be able to find a single solution but will be able to reduce to either a single equation in l, m, and n (if the matrix has rank two) or two equations relating them (if it has rank 1). In the first case, you can include your constraint with the single equation to get a one parameter solution, in the second, you can add it to the two equations to get three conditions that you can solve for a specific point (since that constraint is quadratic, there may be no solution).

3. The determinant is nonzero: I get -20.032. That means the only solution is the trivial solution (l,m,n) = (0,0,0), which cannot satisfy the condition of being on the unit sphere, as HallsofIvy mentioned.