Exercise 1.1.20

Question

Show that equation $(*)$ produces $M=\left[\frac{1}{2}\right]$ in the small example above.

Neil Z. · Accepted Answer

We have $C=\begin{bmatrix}2\3\end{bmatrix}$,
$R=\begin{bmatrix}2 & 4 \end{bmatrix}$, so
$$C^TC= \begin{bmatrix}2&3\end{bmatrix}\begin{bmatrix}2\3\end{bmatrix} = 13,$$
and
$$RR^T=\begin{bmatrix}2&4\end{bmatrix}\begin{bmatrix}2\4\end{bmatrix} = 20, \quad C^TAR^T = \begin{bmatrix}2&3\end{bmatrix}\begin{bmatrix}2&4\3&6\end{bmatrix}\begin{bmatrix}2\4\end{bmatrix}=130.$$
Thus, we get
$$M=(C^TC)^{-1}(C^TAR^T)(RR^T)^{-1} = \frac{1}{13}130\frac{1}{20}=\frac{1}{2}$$

Exercise 1.1.20

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Exercise 1.1.20

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