You are asked to do this problem and you do not know the basic definitions? Do you not have a textbook you could look them up in?
A set of vectors is said to be "independent" if no one of them can be written as a linear combination of the others. Another way of putting that is that \(\displaystyle \{v_1, v_2, \cdot\cdot\cdot, v_n\}\) is an independent set of vectors if and only if, whenever \(\displaystyle a_1v_1+ a_2v_2+ \cdot\cdot\cdot+ a_nv_n = 0\) then we must have \(\displaystyle a_1= a_2= \cdot\cdot\cdot= a_n= 0\).
A set of vectors is said to "span" a vector space if and only if every vector in that space can be written as a linear combination of vectors in that set. That is, \(\displaystyle \{v_1, v_2, \cdot\cdot\cdot, v_n\}\) span vector space, V, if and only if whenever v is in V, there exist numbers \(\displaystyle \{a_1, a_2, \cdot\cdot\cdot, a_n\}\) such that \(\displaystyle v= a_1v_1+ a_2v_2+ \cdot\cdot\cdot+ a_nv_n\).
A basis for a vector space is a set of vectors that both span the space and are independent. That means that every vector in the vector space can be written as a linear combination of the vectors in the basis in a unique way.
