Answer:
v - w - 1
Step-by-step explanation:
Try an experiment with a small, specific set of numbers like:
4, 5, 6, 7, 8, 9, 10 w = 4 and v = 10.
There are 5 numbers in the list, not counting the first and last. Is this related to the difference between v and w? v - w = 6, one more than 5.
The number of natural numbers between w and v, not including w and v, is v - w - 1.
Answer:
![A * B = \left[\begin{array}{ccc}10&-6\\8&5\\19&-10\end{array}\right]](https://tex.z-dn.net/?f=A%20%2A%20B%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%26-6%5C%5C8%265%5C%5C19%26-10%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Given
![A =\left[\begin{array}{cc}2&-2\\3&4\\4&-3\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-2%5C%5C3%264%5C%5C4%26-3%5Cend%7Barray%7D%5Cright%5D)
![B = \left[\begin{array}{cc}4&-1\\-1&2\end{array}\right]](https://tex.z-dn.net/?f=B%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-1%5C%5C-1%262%5Cend%7Barray%7D%5Cright%5D)
Required

To do this, we simply multiply the rows of A by the column of B;
So, we have:
![A * B = \left[\begin{array}{ccc}2*4 + -2*-1&2*-1+-2*2\\3*4+4*-1&3*-1+4*2\\4*4-3*-1&4*-1-3*2\end{array}\right]](https://tex.z-dn.net/?f=A%20%2A%20B%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%2A4%20%2B%20-2%2A-1%262%2A-1%2B-2%2A2%5C%5C3%2A4%2B4%2A-1%263%2A-1%2B4%2A2%5C%5C4%2A4-3%2A-1%264%2A-1-3%2A2%5Cend%7Barray%7D%5Cright%5D)
![A * B = \left[\begin{array}{ccc}10&-6\\8&5\\19&-10\end{array}\right]](https://tex.z-dn.net/?f=A%20%2A%20B%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%26-6%5C%5C8%265%5C%5C19%26-10%5Cend%7Barray%7D%5Cright%5D)