Someone argues: "The coefficient matrix of the system x + y + z = 6, 2x + 2y + 2z = 12
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Linear algebra and vector spaces · Linear algebra and vector spaces
Mathematical Methods for Physics, Ch Matrices, determinants and systems of linear equations
Problem
Someone argues: "The coefficient matrix of the system x+y+z=6,2x+2y+2z=12,x−y+z=2 has determinant zero, so this system has no solution."
((a)) Check the claimed determinant.
((b)) Decide whether the conclusion "no solution" is correct, and if not, find every solution.
((c)) State, in general, what a zero determinant does and does not tell you about a system of three equations in three unknowns.