Find each sum or difference, if possible. See Examples 2 and 3. <1x2 Matrix> - <1x3 Matrix>

Verified step by step guidance

1. insert step 1> Identify the matrices involved in the operation. The first matrix is a 1x2 matrix, and the second matrix is a 1x3 matrix.
2. insert step 2> Recall that matrices can only be added or subtracted if they have the same dimensions.
3. insert step 3> Compare the dimensions of the two matrices. The first matrix has dimensions 1x2, and the second matrix has dimensions 1x3.
4. insert step 4> Since the matrices do not have the same dimensions, it is not possible to perform the subtraction operation.
5. insert step 5> Conclude that the sum or difference of matrices with different dimensions is undefined.

Key Concepts

Matrix Addition and Subtraction

Matrix addition and subtraction involve combining two matrices of the same dimensions by adding or subtracting their corresponding elements. For example, if A is a 1x2 matrix and B is a 1x2 matrix, the result of A + B is another 1x2 matrix where each element is the sum of the corresponding elements from A and B. However, matrices must have the same dimensions to perform these operations.

Matrix Dimensions

The dimensions of a matrix are defined by the number of rows and columns it contains, expressed as 'rows x columns'. For instance, a 1x2 matrix has 1 row and 2 columns, while a 1x3 matrix has 1 row and 3 columns. Understanding matrix dimensions is crucial because operations like addition and subtraction can only be performed on matrices with identical dimensions.

Compatibility of Matrices for Operations

For matrix operations such as addition and subtraction to be valid, the matrices involved must be compatible in terms of their dimensions. This means that both matrices must have the same number of rows and columns. In the given question, a 1x2 matrix cannot be directly subtracted from a 1x3 matrix because their dimensions differ, making the operation impossible.