This example finds the basic solutions for the linear least squares problems where $b_1$ and $b_2$ are the columns of the matrix $B$, A $QR$ factorization is performed on the first $4$ rows of $A$ using zgeqrt after which the first $4$ rows of $B$ are updated by applying $Q^T$ using zgemqrt. The remaining row is added by performing a $QR$ update using ztpqrt; $B$ is updated by applying the new $Q^T$ using ztpmqrt; the solution is finally obtained by triangular solve using $R$ from the updated $QR$.