Addition of Matrices
Key Questions

You add the corresponding elements to get your result.
This is one of the easier matrix operations. Here is an example:
[a b c]+[g h i] = [a+g, b+h, c+i]
[d e f].. [j k l] ... [d+j,. e+k,. f+l]Ignore the "."; it's the only way to space things right now.
Since we are adding corresponding elements, the matrices must have the same dimensions; the answer must also have the same dimension.

The 4x4 matrix :
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
and this one
1 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
are equivalent, because they are both of rank 1.
Actually : two nxp matrices A and B are equivalents iff rank(A) = rank(B).
NB. rank(A) is the dimension of space engendered by the columns of A.

A matrix is a table of numbers (or other elements) disposed in rows ans columns.
For example:
#A=# #((1,2,3),(3,4,6))#
This is a rectangular matrix called#A# with#2# rows and#3# columns, so you say thart#A# has order#2xx3# (2 by 3).You can have square matrices when the numbers of rows is equal to the number of columns:
#B=# #((1,2,3),(3,4,6),(3,2,1))#
Where#B# is a square matrix od order#3xx3# or simply#3# .You can also have matrices with one column only or one row only :
#C=# #((1),(6),(7))# or#D=# #((1,2,3,4,6))#
these are sometimes called vectors or column vector and row vector.A bank statement is an example of a matrix: