1. The problem statement, all variables and given/known data Can the equation x^2 + y^2 + z^2 = 3, xy + tz = 2, xz + ty + e^t = 0 be solved for x, y, z as C^1 functions of t near (x, y, z, t) = (-1, -2, 1, 0)? 2. Relevant equations 3. The attempt at a solution The mixed-partial derivatives matrix I got was: [2x, 2y, 2z, 0] [y, x, t, z] [z,t,x, y+e^t] Plugging in the numbers I get: [-2, -4, 2, 0] [-2, -1, 0, 1] [1, 0, -1, -1] I know the theorem states that when this matrix is invertible, it means explicit functions exist, however, how should I proceed as the matrix is not square?