Ahomogeneous equation is always consistent. a. false. a homogenous equation can be written in the form axequals0, where a is an mtimesn matrix and 0 is the zero vector in set of real numbers r superscript m. such a system axequals0 always has at least one solution, namely, xequals0. thus a homogenous equation is always inconsistent. b. false. a homogenous equation can be written in the form axequals0, where a is an mtimesn matrix and 0 is the zero vector in set of real numbers r superscript m. such a system axequals0 always has at least one nontrivial solution. thus a homogenous equation is always inconsistent. c. true. a homogenous equation can be written in the form axequals0, where a is an mtimesn matrix and 0 is the zero vector in set of real numbers r superscript m. such a system axequals0 always has at least one nontrivial solution. thus a homogenous equation is always consistent. d. true. a homogenous equation can be written in the form axequals0, where a is an mtimesn matrix and 0 is the zero vector in set of real numbers r superscript m. such a system axequals0 always has at least one solution, namely, xequals0. thus a homogenous equation is always consistent.