Question

If matrix D is a 7 x 4 matrix, and the product of matrix D and matrix E, DE, exists, what could be the order of matrix E? 00 4 x 7 4 × 4 7 x 5 7x4 4 x 5 7 x 7​

Answer 1

Explanation:

If matrix D is a 7 x 4 matrix, and the product of matrix D and matrix E, DE, exists, the order of matrix E could be 4 x 4. To understand why, let's break down the matrix multiplication process. When multiplying matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In this case, matrix D has 4 columns. For the product DE to exist, matrix E must have 4 rows. This is because the number of rows in matrix E should match the number of columns in matrix D. Therefore, the order of matrix E could be 4 x 4. It's important to note that while a 4 x 4 matrix is one possible order for matrix E, there could be other valid orders as well. As long as the number of rows in matrix E matches the number of columns in matrix D, the product DE will exist.