Explain what the null space of the coefficient matrix A is in terms of the linear system

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Explain what the null space of the coefficient matrix A is in terms of the linear system

An mxn matrix A can be used to represent a system of m equations with n unknowns. The null space of A is the set {x in R^n| Ax=0}, in other words it is the set (it is actually a subspace of R^n) of all vectors in R^n that when multiplied by the matrix A, yield the zero vector in R^m. So in terms of a linear system of equations, the null space consists of all vectors that are the solution to the homogenous system Ax=0