Answer:
b. 5x6
Step-by-step explanation:
Since we know that in order for a matrix multiplication to be defined, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
We have been given the dimensions of a matrix as: 3 by 5, which means that the number of rows in the given matrix is 3 and number of columns is 5.
In order to multiply our matrix F with another matrix, the number of rows in the another matrix must be equal to 5.
Now let us see our given choices one by one.
a. 3x5
Upon looking at our first option we can see that number of rows in this matrix is 3 and number of columns of our matrix F is 5. 3 is not equal to 5, therefore, option a is not a correct choice.
b. 5x6
Number of rows of the matrix provided in option b is 5 and number of columns of our matrix F is also 5, therefore, option b is the correct choice.
c. Since we know that multiplication of matrices is possible with compatible dimensions, therefore, option c is not a correct choice.
d. As we already found our correct option, therefore, 'none of the choices work' is not a correct choice.
