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Suppose the sum 𝐴 + 𝐵 + 𝐶 exists. We also know that 𝐴 has 2 rows and 𝐶 has 3 columns. What can we say about matrix 𝐵?

Suppose the sum 𝐴 plus 𝐵 plus 𝐶 exists. We also know that 𝐴 has two rows and 𝐶 has three columns. What can we say about matrix 𝐵?

We begin by recalling that in order to perform matrix addition, each matrix must have the same order. This means they must have the same number of rows and columns. Since matrix 𝐴 has two rows, matrix 𝐵 must have two rows. In the same way, since matrix 𝐶 has three columns, matrix 𝐵 must have three columns. All three of the matrices 𝐴, 𝐵, and 𝐶 must have two rows and three columns. We can therefore conclude that 𝐵 is a two-by-three matrix.

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