## Find a Basis of the Subspace of All Vectors that are Perpendicular to the Columns of the Matrix

## Problem 40

Find a basis for the subspace $W$ of all vectors in $\R^4$ which are perpendicular to the columns of the matrix

\[A=\begin{bmatrix}

11 & 12 & 13 & 14 \\

21 &22 & 23 & 24 \\

31 & 32 & 33 & 34 \\

41 & 42 & 43 & 44

\end{bmatrix}.\]

(*Harvard University Exam*)