The statement "Every homogeneous system of linear equations has a solution" is definitively true. A homogeneous system is characterized by having all constant terms equal to zero, which guarantees at least one solution, namely the trivial solution where all variables equal zero. This conclusion is supported by the fact that homogeneous systems are never inconsistent, ensuring the existence of solutions in all cases.
PREREQUISITESStudents of linear algebra, educators teaching mathematical concepts, and anyone interested in understanding the foundational principles of systems of equations.
Math100 said:Homework Statement
(True or False) Every homogeneous system of linear equations has a solution.
Homework Equations
None.
The Attempt at a Solution
Considering that homogeneous system of linear equations are never inconsistent, the statement must be true, right?
You tell us.Math100 said:Yes, so this statement is true?
Right.Math100 said:It's true.