Let A : R -- RM defined by an m X 12 - matrix such that A : VH AV . ( 1) Show that the range R ( A ) is the span of the column vectors of A ;...

Solve question 1 Advanced Linear Algebra related to Vector spaces , Range and Null space . Try to give the solution with detailed necessary steps. Thank u.

1 . Let A : R" -- RM defined by an m X 12 - matrix such that A : VH AV .( 1) Show that the range R ( A ) is the span of the column vectors of A ;( 2) Show that the mull space N ( A ) = 10; if and only if the column vectors of A arelinearly independent .