Let A be a 4x6 matrix and B be a 6x3 matrix. The entries in both A and B are from the set of rational numbers. How many entries does the matrix AB have?

## AnswerThe product of two matrices, A and B, is a new matrix, AB. The dimensions of this new matrix are determined by the dimensions of the original matrices. In this case, matrix A is a 4x6 matrix and matrix B is a 6x3 matrix. When you multiply these two matrices together, the resulting matrix AB will have dimensions determined by the number of rows in A and the number of columns in B.So, the resulting matrix AB will be a 4x3 matrix.The total number of entries in a matrix is given by the product of the number of rows and the number of columns. Therefore, the matrix AB will have 4 * 3 = **12 entries**.Here is a visual representation of the multiplication:| A (4x6) | x | B (6x3) | = | AB (4x3) ||---------|---|---------|---|----------|| | | | | || | | | | || | | | | || | | | | |Each cell in the resulting AB matrix represents a single entry, and there are 12 such cells, hence 12 entries.