query on linear algebra regarding checking of whether a set if vectors is linearly independent or not Will the following set of vectors $a+b$, $c+ d$ ,$d+ e$ and $a + b$ be linearly independent . Here $a+ b$ occurs twice. So will that make it linearly dependent? 

First, rename the vectors: 
$v_1:=a+b$, $v_2:=c+d$, $v_3 :=d+e$. You now have the set of $$\{v_1, v_2, v_3, v_1\}, $$ which is linearly dependent, since you could choose
$$x=\begin{pmatrix}1&0&0&-1\end{pmatrix}^T$$ as linear combination-coefficients. 
This will turn the combination into zero and make the set linearly dependent. 
