Answer to Question #335846 in Linear Algebra for Tannu

Question

let a be a 2 cross 3 matrix b be a 3 cross 4 Matrix and C be 3 cross 2 Matrix and d be a 3 cross 4 matrix. is ab + ctd defined? justify your answer.

Answer 1

A matrix can be multiplied by any other matrix that has the same number of rows as the first has columns. So we can multiply matrices a of dimension 2 by 3 and b of dimension 3 by 4. In the result matrix ab will have a dimension 2 by 4. 

We can transpose a matrix c of dimension 3 by 2 by switching its rows with its columns. So matrix at will have a dimension 2 by 3.

so we can multiply matrices ct and d , because ct has the same number of columns as matrix b has the rows. In the result we will have matrix ctd of dimension 2 by 3.

in the end, we can add matrix ab ( 2 by 4) and matrix ctd ( 2 by 4) , because they has the same number columns and rows. 

so matrix ab+ ctd is defined and will have dimension 2 by 4.