Final answer:
The size of the resulting matrix after multiplying a 1x3 matrix by a 3x3 matrix is a 1x3 matrix; therefore, none of the options provided (1x1, 2x2, 3x3, or 4x4) are correct.
Step-by-step explanation:
The question asks about the size of the matrix resulting from the multiplication of given matrices. When multiplying matrices, the size of the resulting matrix is determined by the number of rows of the first matrix and the number of columns of the second matrix. In this case, the first matrix is 1x3 (one row and three columns) and the second matrix is 3x3 (three rows and three columns). The resulting matrix after multiplication would have the same number of rows as the first matrix and the same number of columns as the second matrix.
Hence, the size of the resulting matrix is 1x3 multiplied by 3x3 which will give us a 1x3 matrix. Therefore, none of the given options (1x1, 2x2, 3x3, or 4x4) are correct. The size of the resulting matrix will be a 1x3 matrix.