Matrices can be added and subtracted if they have the same dimensions. The sum and the difference of two m* n matrices is an m* n matrix.

• Each element of the sum matrix is the sum of the elements of the original two matrices in the same position.

a_(11)&⋯&a_(1n) ...&⋱&... a_(m1)&⋯&a_(mn) + b_(11)&⋯&b_(1n) ...&⋱&... b_(m1)&⋯&b_(mn) = a_(11)+b_(11)&⋯&a_(1n)+b_(1n) ...&⋱&... a_(m1)+b_(m1)&⋯&a_(mn)+b_(mn)

• Each element of the difference matrix is the difference of the elements of the original two matrices in the same position.

a_(11)&⋯&a_(1n) ...&⋱&... a_(m1)&⋯&a_(mn) - b_(11)&⋯&b_(1n) ...&⋱&... b_(m1)&⋯&b_(mn) = a_(11)-b_(11)&⋯&a_(1n)-b_(1n) ...&⋱&... a_(m1)-b_(m1)&⋯&a_(mn)-b_(mn) Click on the elements of the sum and difference matrices below to see the illustration of how these operations work on 3* 2 matrices.