I have two vectors $~A = (a_1,a_2,a_3,a_4, \cdots, a_n)~$ and $~B = (b_1,b_2,b_3,b_4, \cdots, b_n)~$ which are linearly independent, (both compoenents are different from zero)
I want to know if:
$~A = (a_1,a_2,a_3,a_4, \cdots, a_n)~$ will be linearly independent to $~B'=(b_1,b_2, 0,0,0,\cdots,0)~$ ?
where only $~b_1,~b_2~$ are non null and the rest of the elements is equal to zero.
I need to have a linearly independent vector to $~A~$ where only the first elements are non-null, and the rest is null.
Thank you.