(Solved): (a) Consider the following matrix: A=(12131415) (i) Find the nullity of the matrix A. ...

(a) Consider the following matrix: $$A=\left(\begin{array}{llll}1& 1& 1& 1\\ 2& 3& 4& 5\end{array}\right)$$ (i) Find the nullity of the matrix $$A$$. (ii) Given the nullity of $$A$$, we now have the dimension of its nullspace. Find a basis for $$N(A)$$. (iii) What is the rank of $$A$$ ? (b) Consider the following matrix: $$B=\left(\begin{array}{ccc}2& ?1& 9\\ 0& 3& ?15\\ 5& 2& 0\end{array}\right)$$ (i) Find the rank of the matrix. (ii) Find the nullity of $$B$$ and a basis for its nullspace.