LINEAR ALGEBRA :

                                  CALCULATING INVERSE OF A MATRIX

IMP : Check for the determinant. if det =0, then det does not exist AND that matrix is called as SINGULAR MATRIX.

Inverse of 2*2 matrix A :

Inverse of a 3*3 matrix 

SOLVING LINEAR EQUATIONS USING MATRICES :

SPAN of vectors:

Span of vector a : (constant=c)*a(vector) = c*a

scale (vector a) up an down. all the resulting vectors will be span of (vector) a.

For vectors to be represented as linear combinations of all of the 'n' other vectors in R(sub)n, then it is only possible if these n vectors are not collinear (ie these n vectors must not lie in the same line (graphically)).

IF the n vectors are collinear, then not all vectors in R(sub)n can be represented as linear combinations of these n vectors.  

[refer : https://www.youtube.com/watch?v=Qm_OS-8COwU&index=15&list=PLFD0EB975BA0CC1E0 ]

SPAN of vectors {v1, v2, v3, ........, v(sub)n } is the linear combinations of {v1, v2, ......, v(sub)n}

 that is : span = c1v1 + c2v2 + ......... + c(sub)n v(sub)n = any vector in R.