Final answer:
When multiplying matrices of unequal sizes, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix will have dimensions m x p. To find the elements of the resulting matrix, perform dot products of the corresponding rows and columns.
Step-by-step explanation:
When multiplying matrices of unequal sizes, it is important to note that the number of columns in the first matrix must be equal to the number of rows in the second matrix. If the first matrix has dimensions m x n and the second matrix has dimensions n x p, the resulting matrix will have dimensions m x p. To multiply the matrices, we will perform dot products of the corresponding rows and columns. The element in the resulting matrix at row i and column j will be the dot product of the i-th row of the first matrix and the j-th column of the second matrix. For example, if we have a 2 x 3 matrix and a 3 x 2 matrix, the resulting matrix will have dimensions 2 x 2. To find the element at row 1 and column 2 of the resulting matrix, we take the dot product of row 1 of the first matrix and column 2 of the second matrix.