Basis & Dimension : Linear Algebra : Degree #Basis #& #Dimension #: #Linear #Algebra #: #Degree
For a video explanation, click here 👉 https://youtu.be/3ByCs2ILhgo Basis : A non-empty set S in a vector space V ( F ) is said to be a basis of V if i ) S is linearly independent and ii ) S spans V i.e. L ( S ) = V . Note : * In the above definition of a Basis, the second condition L ( S ) = V means every vector in V is a linear combination of vectors of S. * For the two dimensional Euclidean Space R 2 , for ( a , b ) in R 2 ,we have ( a , b ) = a ( 1 , 0 ) + b ( 0 , 1 ) i.e. every element in R 2 , is a linear combination of S = { ( 1 , 0 ) , ( 0 , 1 )...