00:01
All right, i just completed number 29, and it took a long time.
00:06
So i'm going to see if i can make this faster somehow.
00:10
So we do need to know if we're going to determine the inverse of this using the adjoint method.
00:18
We do need to know the determinants of all of the minors.
00:27
So let's try that.
00:28
Minor 1 -1 unfortunately my screen is lagging right now but minor 1 -1 is 1 -3 negative 3 oh my goodness is really lagging negative 3 negative 5 2 all right so i i don't think there's a faster way to do this one.
01:55
So i'm just going to write down the one -three, negative 3 -5.
02:05
And if my screen is going to keep lagging like this, it's going to take forever.
02:16
And then the last one, that's a negative 4 down there.
02:18
It's hard to read.
02:39
Okay, with this screen lagging so much, it's very difficult.
02:51
Okay, 1 times negative 5 times 6 is negative 30.
03:14
3 times 2 times negative 4.
03:19
That would be 6 times negative 4, which is negative 24.
03:37
Negative 3 times negative 3 times 4.
03:42
That's going to be positive.
03:44
3 times 3 is 9 times 4.
03:48
It's 36.
04:06
Okay, now to the minus ones.
04:09
Negative 3 times negative 5 times negative 4.
04:14
And we need to subtract that.
04:17
So that's going to give me a positive.
04:23
And five times four is 20, times three is 60.
04:41
Okay.
04:42
We also have negative 1 times 2 times 4.
04:48
So that's going to be negative 8.
04:50
I'm going to write that on the top here.
04:54
Try to conserve room.
05:01
And last one.
05:04
Minus 3 times negative 3 times 8.
05:08
So that's going to give me a plus.
05:14
3 times negative 3 times 6.
05:16
3 times 3 is 9.
05:20
And 6 times 9 is 54.
05:26
All right, let's put that in a calculator.
05:36
Negative 8 plus 54 minus 30, minus 24 plus 24 plus 36 plus 6, 36 plus 60, 88.
06:25
Okay, so minor 1 -1 is 88.
06:30
Let's just make sure i didn't make any mistakes.
06:35
Negative 30, negative 24, positive 36, plus 60, minus 8, plus 54.
07:22
Okay, so that's minor one -one.
07:25
Let's do minor one, two.
07:50
Scroll down a little bit.
08:26
Okay, one two.
08:31
That's going to be 0 .3, negative 3.
08:51
Um, negative 2, negative 5, 2.
09:20
4 .4 .6.
09:43
I think even with this lag, it's better than writing with a mouse, but it is very frustrating.
10:54
Okay, three times two times four.
11:17
Negative, three times two times four, minus 24.
11:30
Minus 24.
11:38
Minus three times five times four.
11:43
That's minus 60.
11:58
Next one's going to give me zero.
12:03
Six times two times three.
12:06
That's 36.
12:23
Okay, so 20.
12:24
24, minus 24, minus 60, minus 36, that's going to give us negative 96.
12:34
Come on, write faster, please.
12:57
All right, let's check this with green.
13:07
0, 24, negative 24, minus 60, 0.
13:35
Uh -oh.
13:38
That's minus negative 36.
13:47
Minus, because that's a negative 2 in there, that should be positive.
14:21
Yeah, that should indeed be positive.
14:23
So it should actually be negative 60 plus 36, which is negative 24.
14:58
For this very long problem, this is going to be nearly intolerable if this thing keeps lagging.
15:21
M13, which is ridiculous.
15:56
Thinking about what i can do to make this fast.
16:00
But i'm going to close microsoft excel where i have the answers because i actually did this problem in excel.
16:12
Maybe that'll help a little.
16:17
I'm going to go ahead and close microsoft outlook, too.
16:20
Maybe that'll help.
16:35
Okay, m13.
16:40
01 -9 -3.
16:44
Of course, that didn't seem to help yet.
16:56
Negative 2, negative 2.
17:46
It should be a negative 3 in there.
18:02
And the last one, 4 -4 -6.
19:14
All right.
19:16
I'm thinking about just doing these on paper because this thing is lagging so much.
19:22
You know how to calculate determinants.
19:25
So i'm going to finish this one on here, but then i'm going to do them on paper and just write down what the determinants of the minor minors are.
19:42
So, m13 is going to give you, um, is that a six down there? yeah, that's a six.
19:52
Okay, so zero, two times, one times two times four is eight.
20:04
Negative three times negative two times negative two times negative four is negative.
20:12
Three times two is six times four is 24.
20:26
Okay.
20:27
Next.
20:28
Um negative three times negative three times positive four um so it's going to be subtracting three times three times three is nine times four it's 36 okay zero for the next one one times two times six it's 12 plus 12 all right put that in a calculator eight minus 24 minus 36 plus 12 is negative 36.
21:59
All right.
22:02
So this is indeed getting frustrating.
22:10
So what i'm going to do now is i'm just gonna write down m of 1 -4.
22:30
And then i'm gonna write down all of the minors.
22:36
At least i'm intending to.
23:11
Okay, so i'm going to do this on paper using the exact same method, m14.
23:38
1 -4.
23:41
So i need to write down 0 -1 -3, negative 2, negative 5, 4, negative 4.
23:58
I wrote down the minor, 1 -4, and now i need to take the determinant.
24:21
So m -1 -4 is going to give us 48.
24:29
So i hope you were able to do that on your paper.
24:40
Okay, m -21, 0 -0 -1, negative 3, negative 5, 2, negative 4, 4, 6.
25:12
0 -01, negative 3, negative 5, 2, negative 4, 6.
25:27
So take some time to do that on your paper.
25:50
And i get the answer of negative 32.
26:03
This lag is ridiculous.
26:37
Okay, so now we want to do m2.
26:41
So that's going to give me m22.
26:49
0 -01, negative 2, negative 5, 2.
27:03
And then the last one is going to be 4, 46.
27:30
Go ahead and do that on paper.
28:00
I got 12.
28:18
So, all right, i would like to go back to m12.
28:48
That's why i scrolled down a little, because i'm thinking there's a mistake in here in m12.
28:53
So if we go down the diagonals again, i get, i have trouble seeing that number that's in the bottom there.
29:12
Okay, that's zero.
29:15
Three times two times four, it's 24.
29:23
Negative three times negative two.
29:26
Oh, that's a negative two there.
29:30
Three times two times four is 24.
29:31
Negative three, negative two times 24 is also 24.
29:37
So i should have a plus there.
29:41
And then minus 60 and plus 36.
29:52
So that actually gives me, well, let's put it in the calculator, 24 plus 24 plus 36, minus 60.
30:09
That's going to give me 24.
30:11
So this should actually be positive 24, as if i can write that.
30:18
Okay, so m1 -2 is positive 24.
30:23
I'm going to do all of these by hand right now.
30:30
So we thought that m -1 -3, i mean on paper right now, because this lag is making it really hard to think.
30:47
So i thought that m -1 -3 was negative 36.
30:56
Let's just verify that it is negative 36.
31:01
So m13 is going to be 0 .1, negative 3, negative 2, negative 3, and 4 -4 -6.
31:45
So that gives me negative 40.
31:49
So now i've got to look and see where my mistake was.
32:00
Well, first of all, negative three times six times zero.
32:08
That's zero...