0:00
There.
00:01
So for this occasion we got this matrix a and b and we need to show that actually p diagonalize a.
00:08
That means that we can obtain a matrix d after applying the inverse of p times a times b.
00:18
And this matrix d should be diagonal.
00:21
So that's what we need to prove first.
00:25
So to check that, we need to first calculate the inverse of this matrix b.
00:31
So the inverse of b is equals to 0 minus 5.
00:39
1, 1 4 minus 1, and 010.
00:46
And then we can calculate d.
00:49
So d is going to be equals to 0 minus 5, 1, 4 minus 1, 010, the matrix a and the matrix b.
01:12
And one zero one one zero five and after multiplicating all these matrices you obtain that the d is equal to minus two zero zero zero minus one zero one so as you can observe this is a diagonal matrix so yes p diagonalize a great now with all this information, we need to compute a, a to the 10 power.
02:02
How? well, given that we got this matrix p and d, where d is diagonal, then we can calculate a to the 11 power, sorry, as p inverse, sorry, here is just p, yes, p, d, and the inverse of p.
02:36
And we got all these matrices...