Solve question 1 Advanced Linear Algebra related to Vector

Question

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 : Rquot; — 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 are
linearly independent .
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