# Math Help - Full Column rank of a partitioned matrix

1. ## Full Column rank of a partitioned matrix

Suppose matrix X is partitioned into $X=[A \ \ \ B]$ where A is $n \times k_1$ and B is $n \times k_2$

How can I show that if $X$ has full column rank, then $X_2$ will have full column rank as well

2. Hello

Note, that since $X$ has full column rank, all their columns are linearly independent as vectors; any subset of a linearly independent set of vectors, is linearly independen too. From this your result follows inmediately.

Best regards.