High School

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?

A. 4 x 7
B. 4 x 4
C. 7 x 5
D. 7 x 4
E. 4 x 5
F. 7 x 7

Answer :

Final answer:

Matrix D is a 7 x 4 matrix. The order of matrix E in the product DE must be 4 x 4.

Explanation:

Matrix D is a 7 x 4 matrix. The order of a matrix represents the number of rows and columns in that matrix. If the product of matrix D and matrix E, DE, exists, the number of columns in matrix D must be equal to the number of rows in matrix E for the product to be defined.

Since matrix D is 7 x 4, the number of columns is 4. Therefore, matrix E must have 4 rows in order for the product DE to exist. The order of matrix E could be 4 x 4.

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