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. D-A

Verified step by step guidance

1. Identify the matrices D and A. Ensure you have the correct dimensions for each matrix.
2. Check if the matrices D and A have the same dimensions. Matrix subtraction is only possible if both matrices have the same number of rows and columns.
3. If the dimensions match, proceed to subtract matrix A from matrix D. This involves subtracting each element of matrix A from the corresponding element of matrix D.
4. Write out the resulting matrix after performing the subtraction for each corresponding element.
5. If the dimensions do not match, state that the operation is not defined because matrix subtraction requires matrices of the same dimensions.

Key Concepts

Matrix Operations

Matrix operations include addition, subtraction, and multiplication of matrices. For addition and subtraction, matrices must have the same dimensions, meaning they must have the same number of rows and columns. Understanding these operations is crucial for performing calculations involving matrices, as they dictate how matrices can be combined or manipulated.

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. When performing operations like addition or subtraction, it is essential to ensure that the matrices involved have the same dimensions; otherwise, the operation is undefined.

Defined Operations

An operation between matrices is defined only when the matrices involved meet specific criteria, such as having compatible dimensions. For instance, subtracting two matrices is only possible if both matrices have the same dimensions. If the criteria are not met, the operation cannot be performed, and it is important to state the reason for this limitation.