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ANSC*6370 QG and Animal Models
Fall 03 - Quiz 3 - Answers

1.

Define what is meant by the symbol $\sigma^{2}_{21}$ in terms of nonadditive genetic variances. Show a picture if that helps.

This represents an additive by additive by dominance genetic interaction

2.

Let ${\bf A}$ be a rectangular matrix with r rows and c columns, and let ${\bf B}$ be a rectangular matrix with p rows and q columns, then explain the following:

(a)

In order for ${\bf A}$ and ${\bf B}$ to be conformable for addition then, ... r=p and c=q.

(b)

In order for ${\bf A}$ and ${\bf B}$ to be conformable for multiplication then, ...

c=p must be true.

(c)

The product ${\bf AA}'$ is symmetric because ...

$$({\bf AA}')' = ({\bf A}')'({\bf A})' = {\bf AA}'$$

(d)

If ${\bf A}$ and ${\bf B}$ are both square, then the product ${\bf AB}$ would be equal to the product ${\bf BA}$ under what circumstances?

A general case would be when both matrices are diagonal. There could be other special cases, like ${\bf B}={\bf A}$.