In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. A+D

Key Concepts

Matrix Addition

Matrix addition involves combining two matrices of the same dimensions by adding their corresponding elements. For example, if A is a 2x2 matrix and D is also a 2x2 matrix, the resulting matrix from A + D will also be a 2x2 matrix, where each element is the sum of the corresponding elements from A and D.

Matrix Dimensions

The dimensions of a matrix are defined by the number of rows and columns it contains, expressed as 'm x n' where m is the number of rows and n is the number of columns. For matrix operations like addition to be valid, the matrices involved must have the same dimensions; otherwise, the operation is undefined.

Undefined Operations

An operation is considered undefined when the conditions for that operation are not met. In the context of matrix operations, if two matrices do not share the same dimensions, attempting to add them will result in an undefined operation, meaning it cannot be performed.