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## Homework Statement

Let [tex]\Sigma = [/tex]

( var(X1) cov(X1, X2) )

( cov (X2. X1) var(X2) )

Show that [tex]Var (a_1 X_1 + a_2 X_2) = a^T \Sigma a[/tex]

where [tex]a^T = [a_1 a_2][/tex] is the transpose of the of the column vector a

## Homework Equations

## The Attempt at a Solution

I got this far:

[tex]Var (a_1 X_1 + a_2 X_2) = a_1^2 Var(X_1) + a_2^2 Var(X_2) + 2a_1 a_2 Cov (X_1, X_2) = a_1^2 Var(X_1) + a_2^2 Var(X_2) + a_1 a_2 Cov (X_1, X_2) + a_1 a_2 Cov (X_2, X_1)[/tex]

Thats all I got so far, any hints