Transcript:
Hi, everyone in cycle notation. We have to find the inverse of each permutation and we have six problems here. So the first one, basically all you’re going to do is write 1 3 2 4 5 and we want to find the inverse. So that means you just reverse the order, so it’s going to be 5 4 2 3 1 now. The inverse is, we want to start with writing 1 in the standard position 1 so 1 maps to 5 then 5 maps to 4 4 maps to 2 2 maps to 3 and 3 maps back to 1 So you close it up, OK? For number 2 We have 1 3 2 4 5 inverse now. This equal’s 4/5 inverse composed with 1 3 2 inverse, and that’s because P Q inverse equals Q inverse with P inverse. Remember, permutations are compositions, but sometimes we call them the product or combining or multiplying, so either way, it’s really compositions. So now that we have this, we reverse the order. This is 5 4 and then 2 3 1 Now we want to start our order. One in the lead position, so 1 maps to 2 two maps, two, three, three. Maps back to one so close it up the next number. We’re missing is for you. Go in order. So four four maps to five and five Max back to four, so close it up, Okay, The next one is C, so we have one three, two four five inverse, so we write this as 2 4 5 in verse 1 3 inverse, so just reverse the order 5 4 2 & 3 1 Now to write your permutation out to let one be the lead. We know 1 maps to 3 & 3 maps back to 1 So you close it up. Our next number is 2 2 maps to 5 5 maps to 4 4 maps to 2 Which we have here Massachu. So close it up, Okay, The next one little different. They both have once in it in the previous video. We went over the ones so basically for this one. We want one, two, three one, four five inverse. So that’s going to be one for five in verse 1 2 3 inverse. Now reverse the order, So you get 5 4 1 3 2 1 so for this one, we want one in position 1 so 1 maps to 3 alright 3 maps to 2 and 2 maps to 1 but we have another one here so for that, we’re going to take 1 maps to 5 and 5 maps to 4 and 4 maps back to 1 then close it up because this one, we had 2 ones, so that one’s a little different same things going to happen with. E so for e, we have 1 3 1 4 1 5 inverse, so this is going to be 1 5 in verse 1 4 inverse and 1 3 inverse. Now change up the order, so this is going to be 5 1 4 1 and 3 1 OK, so you start with 1 1 maps to 3 and you’re always going from right to left and 3 goes back to 1 but we have a 1 here, so this 1 maps to 4 4 maps back to 1 but now we have a 1 here, so this 1 maps to 5 and this 5 maps back to 1 so that’s your final answer there, alright? And for the last one we have 1 2 3 1 5 inverse, so that’s 1 5 in verse 1 2 3 inverse. All right, so change the order 5 1 3 2 1 All right, now, let’s see what we can do with this one. So we have start with one in the lead position or position 1 1 maps to 3 3 maps to 2 and 2 maps back to 1 but we already have a 1 here, so this one maps to 5 and this 5 map maps to 1 and we’re done and that’s it. Thank you, have a nice day. Bye bye! [MUSIC].