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I have some trouble understanding the concept of a covariance matrix.

I want to find the covariance of a and b Cov(a,b).

I have a random vector y=(y1, y2, y3)' with mean vector and covariance matrix μ = (1, 0, 2) Σ = ((1,1,0),(1,2,0),(0,2,1)). a,b are defined as a=(a1,a2)' and b=(b1, b2, b3)'

a1= y1 + y2 + 2y3

a2 = y1 + 2y2 - 3y3

b1 = 2y1 - 1y2 + y3

b2 = y1 + y2 - 3y3

b3 = y1 + y2 + 2y3

My first two steps are

Cov(a,b)=Cov((a1,a2)(b1,b2,b3)) =Cov((y1 + y2 + 2y3,y1 + 2y2 - 3y3)(2y1- 1y2 + y3, y1 + y2 - 3y3, y1 + y2 + 2y3))

How to do next?

amflynn
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    Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Sep 20 '21 at 19:32
  • Start by finding $\operatorname{Cov}(a_1,b_1).$ The other five covariances are found the same way, so if you can do this one (the duplicate explains how), you can do the other five. The six answers must be laid out in a $2\times 3$ matrix. That's all there is to it. – whuber Sep 20 '21 at 21:42

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