00:01
Given matrix is a is equal to 1 3 3 minus 3 minus 5 minus 3 3 3 1.
00:10
Therefore, the characteristic equation is determinant of a minus lambda i which is equal to 0 that is 1 minus lambda 3 3 minus 3 minus 5 minus lambda minus 3 3 3 1 minus lambda which is equal to 0.
00:39
Hence, after solving this determinant we get 1 minus lambda into minus 5 minus lambda into 1 minus lambda plus 9 minus 3 into 3 minus minus 3 plus 3 lambda plus 9 plus 3 into minus 9 plus 15 plus 3 lambda is equal to 0 which implies that 1 minus lambda into minus 5 plus 5 lambda minus lambda plus lambda square plus 9 minus 3 into 6 plus 3 lambda plus 3 into 6 plus 3 lambda is equal to 0 which implies that 1 minus lambda into lambda square plus 4 lambda plus 4 minus 18 minus 9 lambda plus 18 plus 9 lambda is equal to 0 which implies that 1 minus lambda into lambda plus 2 square is equal to 0 which gives lambda is equal to 1 or lambda is equal to minus 2.
02:10
Now, for the given eigenvalue lambda is equal to 1.
02:15
A minus lambda i is 1 into i which is given therefore 0 3 3 minus 3 minus 6 minus 3 3 3 0.
02:32
Now, perform an operation that is interchange r1 with r2 we get minus 3 minus 6 minus 3 0 3 3 3 3 0.
02:46
Now, next perform an action r1 is equal to r1 upon minus 3.
02:54
So, the matrix will be 1 2 1 0 3 3 3 3 0.
03:05
Now, next perform an action on r3 such that r3 minus 3 r1.
03:13
So, we get the matrix 1 2 1 0 3 3 0 minus 3 minus.
03:22
Now, next perform an action on r3 as r3 plus r2 we get the matrix 1 2 1 0 3 3 0 0 0.
03:33
Now, next perform an action on r2 is equal to r2 upon 3.
03:40
So, we get the matrix 1 2 1 0 1 1 0 0 0.
03:46
Now, next perform an action on r1 as r1 minus 2 r2.
03:51
So, we get the matrix 1 0 minus 1 0 1 1 0 0 0...