In Exercises 9 - 16, find the following matrices: a. A + B3 1 1 2 - 3 6A = B = - 1 2 5 - 3 1 - 4

Matrix addition involves combining two matrices of the same dimensions by adding their corresponding elements. For example, if A and B are both 2x3 matrices, the resulting matrix C will also be a 2x3 matrix where each element C[i][j] = A[i][j] + B[i][j]. This operation is fundamental in linear algebra and is used in various applications, including solving systems of equations.

The dimensions of a matrix are defined by the number of rows and columns it contains, expressed as 'rows x columns'. For instance, a matrix with 2 rows and 3 columns is referred to as a 2x3 matrix. Understanding matrix dimensions is crucial for performing operations like addition and multiplication, as these operations can only be performed on matrices with compatible dimensions.

Element-wise operations refer to performing calculations on corresponding elements of matrices. In the context of matrix addition, each element from the first matrix is added to the corresponding element in the second matrix. This concept is essential for understanding how to manipulate matrices and is widely used in various mathematical and engineering applications.