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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:
    http://www.dreamstime.com/stock-images-bank-statement-image436784

Questions