00:00Which of following are the symmetric or it's symmetric?
00:05Look, this is a matrix.
00:08The first thing we will do is transform.
00:12The first row is the first column, the second row is the third column,
00:16and the third row is the third column.
00:19Look, the matrix is the same.
00:22It will be symmetric.
00:27What will happen?
00:28It will be symmetric.
00:29But if this doesn't happen, like in this case,
00:32then what do we do?
00:36We will multiply all these terms.
00:40So, minus 5 to 5,
00:44minus 6 to 6,
00:46minus 5 to 5,
00:48minus 7 to 7,
00:49minus 6, minus,
00:51now this is done.
00:52Because this is minus a transpose,
00:55we will multiply all these sentences,
00:56so this Will be symmetric.
00:59Okay, question number 2.
01:01As we have Mitglied matrix here.
01:06Yes, this is a matrixерene stabilisation.
01:09It will Carmichael make turns
01:10itorientated.
01:10it's a matrix.
01:11It will meanύ aiστε 沒有 vest
01:16this ring at a 코 et pour ça.
01:183rd column, 3rd row, 3rd column.
01:23Transpose job,
01:24we have taken it,
01:24this is not equal to a.
01:27We will change all of the sine change.
01:30What do we do?
01:31Minus multiply.
01:32Here we have minus 1.
01:35Here we have minus 1.
01:36Minus 1 is 1.
01:375 is minus 5.
01:39Minus 3 is 3.
01:40Now this is equal to a.
01:42This is because a minus a.
01:45This is equal to a.
01:45This is symmetric.
01:49Now here we have matrix a.
01:51This is transpose.
01:531, 2, 5.
01:542, 5, minus 7.
01:555, minus 7.
01:57If a transpose is equal to a,
01:59then the matrix is symmetric.
02:02Then we have matrix a.
02:04This is transpose.
02:07First row, first column.
02:08Second row, second column.
02:10Third row, third column.
02:12But we have no benefit from this.
02:14Because this is equal to a.
02:16Then we have transpose.
02:17Transpose.
02:18Then we have sin change.
02:19We have minus.
02:20We have minus multiply.
02:22We have minus.
02:23This is minus 5 is 5.
02:244 is minus 4.
02:26Now this is equal to a.
02:27This is equal to a.
02:29Now this is equal to a.
02:30Find the index of the following nilpotent matrix.
02:34So nilpotent.
02:36This is equal to a.
02:41Then we have minus.
02:42Now this is equal to a.
02:512nd column
02:552nd column
02:562nd column
02:572nd column
02:572nd column
02:583rd column
03:000
03:02here we go
03:072nd column
03:080
03:11of course
03:162nd column
03:170
03:190
03:190
03:200
03:200
03:200
03:220
03:230
03:230
03:240
03:240
03:240
03:25Now, when we go to second row, we go to second column, then we go to second column.
03:34Second row, then we multiply the third column.
03:37Now, third row is zero.
03:39How many times do we multiply the zero?
03:42So, there is no potential.
03:44No potential is all zero.
03:46Now, A square, we multiply A by A by A.
03:49Now, A square, we multiply the A by A.
03:54This is the first row of multiplication.
03:59Second column and third column.
04:03The first row of multiplication is zero.
04:04We multiply the zero, zero, zero, zero, zero, zero, zero.
04:10Now, the first row of multiplication is zero.
04:13It's zero, zero, zero, zero, zero, zero, zero, zero.
04:16Then, if I put a zero then, like A square, zero, zero, zero, zero, zero.
04:21And, what is zero, zero?
04:24To do a square then, A square, zero.
04:26A cube, zero.
04:27Then, the real proprietor in세ices are zero.
04:31A square is zero.
04:31The總ors on the A square to A,
04:32Then, a square now, a-c матres is zero.
04:36If this is zero, no mindset unknown.
04:39So now, we can consider this alignment.
04:42Together, I will use another puzzling loop loop loop loop loop loop loop loops.
04:46We have this matrix for 2 times.
04:49This is the first row.
04:501-1, minus 3 into minus 1, plus 3.
04:55Then minus 4 into 1, minus 4.
04:57This is here.
04:58First row.
05:011-3, minus 3, minus 3, minus 9.
05:05Then minus 4, minus 3, minus 12.
05:08First row.
05:111-4, minus 3, minus 4, minus 3, minus 12.
05:15Then minus 4, minus 4, minus 4, minus 16.
05:19Then this row.
05:21Second column.
05:22First, second, third. Second row.
05:24Then third row.
05:26Second row.
05:28Minus 1, minus 1, minus 1.
05:303, minus 1, minus 3, minus 3.
05:334, minus 4.
05:34Then this row.
05:36Minus 1, minus 3, minus 3, minus 3.
05:393 is 9.
05:413 into minus 3.
05:44Then, 4 into minus 3.
05:46Then this row.
05:464, minus 12.
05:48This row.
05:50Minus 1, first row.
05:54Yes, 1.
05:571 and around, minus 4, minus 4.
06:00Then minus 3, minus 3, minus 4, minus 4, minus 4, minus 4, minus 4, minus 4, minus 4, minus
06:054.
06:05Well, then minus 4, minus 4, minus 4, minus 4, minus 4, minus 4, plus 16.
06:07the first row is completed.
06:09This is the second row.
06:11The first column is the answer from the second row.
06:15The second row is the third column,
06:18the third row is the third row.
06:19The third row into the first column,
06:21the third row into the second column,
06:22the third row into the third column.
06:24Look, this determinant is zero,
06:26which is a square.
06:28So this is important matrix.
06:30But now the index is how much?
06:33Question 8,
06:35the second row is the period.
06:37If a square is equal to a,
06:40then period 1.
06:42But if a cube is equal to a,
06:45then period 2.
06:47Now we have a matrix
06:49two times.
06:50This row is the first row.
06:52The column is the first column.
06:541 is the 1,
06:55minus 2 is the 3, minus 6 is the 2.
06:58This one is the 2.
07:00Here we go.
07:03This row is the third row.
07:04Then this row is the first row.
07:06Which will multiply by the other columns?
07:091 is the 2.
07:111 is the 2.
07:122 is the 2.
07:132 is the 2.
07:14And this row is the 2.
07:17Third row is the 3.
07:181 is the 2.
07:211 is the 3.
07:222 is the 3.
07:232 is the 3.
07:329 into 2
07:32Then we go to the second column
07:35Minus 3 into minus 2
07:362 into 2
07:389 0
07:38Then we go to the third column
07:42Third row, first column
07:44Third row, second column
07:44This is all
07:46Now, this is what we have
07:48This is minus 5, minus 6
07:519, 10, 9
07:52Minus 4, minus 4, minus 3
07:54This is a square
07:56We need a cube to do
07:57What do we need to do?
07:58A square
07:59Who will multiply?
08:01A
08:02A square
08:03A square
08:04To get a cube
08:07It will be full
08:08It will be the same
08:10Now, this is a cube
08:11A cube
08:12A cube
08:14Then the created
08:17What will be the same
08:19If A square
08:21A square
08:22What will be the same
08:23So, this time
08:24What will be the same
08:25One
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