Let $A$ be a 5 X 8 matrix whose rank is 3. Computer dim(Nul($A$))

Question

Let $A$ be a 5 X 8 matrix whose rank is 3. Computer dim(Nul($A$))

I believe this problem uses the formula: rank($A$) + dim(Nul($A$)) = n

So would the answer be as simple as: $$3 + x = 8$$ $$x = 8 - 3$$ $$x = 5$$

This also seems too simple to be correct... Any input is appreciated.

Answer 1

Your answer is correct, using the "rank-nullity" theorem. R(A) + N(A) = n