Question

The size of matrices a and b are given. Find the sizes of ab and ba whenever they are defined. (if an answer does not exist, enter dne.) a is of size 6 ✕ 7, and b is of size 7 ✕ 8.

Answer 1

We have been given two matrices a and b. A has 6 rows and 7 columns, while b has 7 rows and 8 columns.

Since we know that order matters in matrix multiplication. In order for matrix multiplication to be defined number of columns in the first matrix should be equal to the number of rows of in the second matrix.

We can see that number of columns in matrix a and number of rows in matrix b is 7.

Therefore, size of ab will be equal to number of rows of matrix a and number of columns of matrix b that is 6 by 8.

Now we will see whether ba is defined or not. We can see columns in matrix b are 8 and rows in matrix a are 6, which is not equal. So we can say that ba is not defined.

Therefore, size of ba is not defined (dne).