00:01
Okay, so we have the following two vector functions, x1 and x2 and the matrix a.
00:09
And we want to show that both of these belong to the system.
00:13
X prime vector is equal to a matrix multiplied by the x vector.
00:19
So what we're going to do first is evaluate these two sides separately.
00:23
And so for x1, we'll try a x1 first.
00:30
And this will give us 1 over t, t negative 1 over t 0, times t sine t, cosine t, which is just, so 1 over t times t sine t gives us sine t, and then plus t cosine t.
00:55
And then we're left with negative 1 over t, sine t, so negative sine t, and 0, cosine t which is just zero and then we'll take the derivative x1 prime to get so we have t sine t and doing product rule that gives a sine t plus t cosine t and then the derivative of cosine t is just negative sine t so for the first part we have a match and now for the second part a x2 or a x2 is just matrix a matrix a is just matrix a matrix a t, negative 1 over t 0 times minus t cosine t and sine t.
01:44
And we'll do matrix multiplication to get negative cosine t minus.
01:54
So we have a positive t and a positive sine t...