Addition of Matrices

If A = [ a_ij ] and B = [b_ij ] are matrices of size m x n, then their sum is the m x n matrix given by

A + B = [a_ij + b_ij ].

The sum of two matrices of different sizes is undefined.

Examples

a. [  -2   3   ]  +   [   4   2   ]    =   [  -2 + 4,  3 + 2  ]   =  [   2   5   ]

    [   5   8   ]       [  -1   3   ]         [ 5 + (-1), 8 + 3  ]       [  4  11   ]

b. [  -1   6   4  ]   +   [   3   1   6   ]    =   [   2   7   10   ]

    [   4   1   5   ]        [  -8   5   3   ]        [  -4   6   8     ] 

c. [ 1 ]      [ 2 ]       [ 3 ]

    [ 7 ]  +  [ 3 ]  =  [10]

    [ 5 ]      [ 4 ]      [ 9 ]

d. The sum of

       [ 5  1 ]                   [  1  2  6  ]

A = [ 2  3 ]  and  B =    [  4  3  8  ]

       [ 1  4 ]                   [ -1  2  0  ]

is undefined. Because the matrices of both A and B have different sizes.