Find the number of 2 x 2 matrices that can be formed by using 1;2; 3; 4 when repetition is allowed
Answers
Step-by-step explanation:
2x2 matrices have 2*2 = 4 spaces to fill elements in.
Lets start form top-right:
it can take any number out of the four so it has
top-right: 4 options
Now going to to top-left:
As top right has already used up one of the number from 1, 2, 3, 4. As we cannot repeat that number, we are only left with 3 options for the top-left so,
top-left: 3 options
Moving onto the bottom-right:
The top row took up 2 of the elements from 1, 2, 3, 4. As we cannot repeat any numbers, we are only left with 2 elements for bottom-right so,
bottom-right: 2 options
Now for the last place(bottom left):
All the other places have been filled so we don’t really have any other options than what will be left so,
bottom-left: 1 option
Now we know how many possible options all the places have while not repeating any number, we can just go ahead and multiply them, so
4*3*2*1 = 24 ways to do it.
Note: You can start from any element of the matrix, it doesn’t have to be in any particular order either.