College Algebra Matrices
Matrix Addition Concepts 1

|  |  | Statement |  |
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If A and B are both m x n matrices, then their sum is the m x n matrix formed by adding the corresponding entries in each matrix. If A = (aij)m x n and B = (bij)m x n, then their sum is A+B = (aij + bij)m x n

We can add only matrices with equal numbers of columns and equal numbers of rows. For example, addition of a 3 x 2 matrix and a 2 x 2 matrix is not defined.

Example. Add the matrices.

The m x n zero matrix, denoted by 0, is the m x n matrix with each entry equal to zero. Since A + 0 = 0 + A = A for every m x n matrix A, the zero matrix is the additive identity for the set of m x n matrices.

The additive inverse -A of the matrix A is (-1)A. Thus, A + (-A) = (-A) + A = 0 for any m x n matrix A.

|  |  | Definition |  |
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To define subtraction of two m x n matrices A and B use the additive inverse as folows: A - B = A + (-B). To subtract B from A we need only subtract the entries in B from the corresponding entries in A.

Properties
A+(B+C)=(A+B)+C | Associative Law
A+B=B+A | Commutative Law
A+0 = 0+A=A | Additive Identity

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