Please send the solution to the problem given in the attachment.

A set B is a basis of V if 1. its elements are linearly independent 2. every element of V is a linear combination of elements of B. Only this two conditions makes basis . Here...

yes it can be....if it is LI set and spanned whole 2D space then this set form a basis

For any vector space there exist infinite bases. In this case if {(a,b),(c,d)} are L.I. or spanning set then it will become basis