Final answer:
To determine the values of 'u' and 'y' for matrix multiplication, we used the fact that the number of columns in the first matrix must equal the number of rows in the second matrix. By setting these equal and solving the equations, we found that 'u' is 1 and 'y' is 2, resulting in 'u' times 'y' as 2.
Step-by-step explanation:
The question involves finding the product of two matrices and is related to the concept of matrix multiplication. For two matrices to be multiplied, the number of columns in the first matrix must equal the number of rows in the second matrix. Given that the order of matrix P is (2u+1) x 2 and the order of matrix Q is (3y-4) x 3, we can deduce that the multiplication PQ is defined, which implies that the number of columns in P (which is 2) is equal to the number of rows in Q (which is 3y-4). To find the value of 'u' and 'y', we set these equal: 2 = 3y-4.
Solving for 'y', we get y = 2. Since QP is also defined, this means the number of columns in Q (which is 3) must be equal to the number of rows in P (which is 2u+1). Therefore, we have the equation 3 = 2u+1. Solving for 'u', we get u = 1. So, the product of 'u' and 'y' (u*y) is 1*2, which gives us the value of 2.