It is true that the null space of a is the solution set of the equation ax = 0.
What is the proof?
The null space of a matrix A is Nul(A)= {x : Ax=0}. In other words, if A is m × n, then its null space consists of those vectors x ∈ Rn which solve the homogeneous equation Ax= 0.
Solving Ax=0 yields an explicit description of Nul(A).
Therefore, the Option A is correct.
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