If c is a fixed vector of size 31, show that var(c U ) = c cov(U

Question:

If c is a fixed vector of size 3×1, show that var(c

U ) = c

cov(U )c and cov(U +

c) = cov(U ).

Comment. If V is an n×1 random vector, C is a fixed m×n matrix, and D is a fixed m×1 vector, then cov(CV + D) = Ccov(V )C

.

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