Question

Select all the correct answers.

If matrix D is a 7x4 matrix, and the product of matrix D and matrix E, DE, exists, what could be the order of matrix E?
1. 4x7
2. 7x4
3. 7x7
4. 7x5
5. 4x5
6. 4x4

Answer 1

3 Answers: 4x7 and 4x5 and 4x4

Step-by-step explanation

Rule: If matrix A is of size m x n and matrix B is p x q, then matrix product AB exists if and only if n = p. Otherwise, AB isn't possible.

So basically the n and p must match up and be the same value.

The number of columns of matrix A must be the same as the number of rows of matrix B.

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Let's use that rule for matrix D and matrix E.

D is 7x4

E is of some unknown size.

But we know that E must have 4 rows or else matrix product DE wouldn't be possible. The number of columns of D (which is 4) must match with the number of rows of E (which must also be 4).

So matrix E could be either 4x7 or 4x5 or 4x4

The 1st number must be 4. The 2nd number can be any positive integer.