Middle School

Suppose A and B are 2 x 5 matrices. Which of the following are the dimensions of the matrix A + B?

A. 2 x 5
B. 10 x 10
C. 7 x 7
D. 7 x 1

Answer :

Answer:

2 x 5

Step-by-step explanation:

When we add matrices, the dimensions of the matrices being added must be the same

A and B are 2 x 5 matrices so they are both 2 x 5 matrices

The output or the sum is also a 2 x 5 matrix

Final answer:

The sum of two 2 x 5 matrices A and B is also a 2 x 5 matrix as matrix addition is done element-wise and requires matrices to have the same dimensions.

Explanation:

When adding two matrices, such as matrix A and matrix B, the dimensionality of the resulting matrix will be the same as that of the individual matrices. Provided that both matrices A and B have dimensions of 2 x 5, their sum, A + B, will also result in a 2 x 5 matrix. This is because matrix addition is defined element-wise, meaning each corresponding entry of the matrices is added together, and thus the size of the matrices must be identical.