Question

If a is a 2x3 matrix and b is a 5x3 matrix, what is the size of the matrix c if c = a * b?

1) 2x5
2) 3x2
3) 4x2
4) 5x5

Answer 1

The multiplication of matrix a (2x3) and matrix b (5x3) is not possible because the number of columns in a does not match the number of rows in b. Therefore, no resultant matrix c can be formed, and none of the options provided for the size of matrix c is correct.

Step-by-step explanation:

When considering the multiplication of two matrices, the number of columns in the first matrix must match the number of rows in the second matrix to perform the multiplication. In the case of matrix a being a 2x3 matrix and matrix b being a 5x3 matrix, the multiplication a * b is not possible because the number of columns in matrix a (which is 3) does not match the number of rows in matrix b (which is 5).

For matrix multiplication to be possible, if matrix X is an m×n matrix and matrix Y is a p×q matrix, n must equal p. The resulting matrix will then have a size of m×q.

In this case, since matrix a has 3 columns and matrix b has 5 rows (which do not match), the multiplication cannot be performed, and thus none of the options presented (2x5, 3x2, 4x2, 5x5) is correct for the size of matrix c.