Question

NOTE: If either of the products is not defined, type UNDEFINED for you answer. If the product is defined, type the dimension in the form mxn with NO spaces in betwee.

Answer 1

a) Dimension of AB is DEFINED

b) Dimension of BA is UNDEFINED

Explanation:

A matrix is always represented with (mxn) rows and columns. the rows are the elements in the horizontal line while the columns make up the elements in the vertical line. however, there are rules in multiplication of matrix.

To multiply matrix, multiply elements in the rows of the first matrix by the elements in the columns of the second matrix. for example if you're multiplying a 3by2 matrix by a 2by3 matrix, the resulting matrix will be a 3by3 matrix from (mxn) -rows and columns.

from the question, matrix A is a 3by5 (3x5) matrix i.e it has 3rows and 5columns.

matrix B is a 5by2 (5x2) matrix i.e it has 5rows and 2columns. multiplying AB = (3x5) X (5x2), hence the resultant matrix will be a 3by2 (3x2) and this shows that multiplication or dimension of AB is DEFINED.

As for the multiplication of BA = (5x2) X (3x5), from this multiplication, it is not possible as such we can't determine any resultant matrix, this makes multiplication or dimension of BA to be UNDEFINED.