Mark each statement True or False. Justify each answer. a. A homogeneous system

Question

Mark each statement True or False. Justify each answer. a. A homogeneous system of equations can be inconsistent. Choose the correct answer below o A. True. A homogeneous equation cannot be written in the form Ax-0, where A is an mxn matrix and 0 is the zero vector in Rm. Such a system Ax-0 does not d B. True. A homogeneous equation can be written in the form Ax-o, where A is an mxn matrix and 0 is the zero vector in Rm. Such a system Ax-o always has at ? c. False. A homogeneous equation can be written in the form Ax-0, where A is an m x n matrix and 0 is the zero vector in Rm. Such a system Ax = 0 always has ? D. False. A homogeneous equation cannot be written in the form Ax = 0 where Ais an m n matrix and s the zero vector n R Such a system Ax does not have the solution x 0. Thus, a homogeneous system of equations can be inconsistent. least one solution, namely x 0. Thus, a homogeneous system of equations can be inconsistent. at least one solution, namely x0. Thus, a homogeneous system of equations cannot be inconsistent. have the solution x 0. Thus, a homogeneous system of equations cannot be inconsistent.

Explanation / Answer

False. Since the zero vector is always a solution, a homogeneous system of equations can never be inconsistent.

Option c is the answer

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