Quantitative Analysis for Management, 13/e

Key Equations

(M5-1)

$$\left(\begin{array}{c}a\\ b\\ c\end{array}\right)\times \left(\begin{array}{cc}d& e\end{array}\right)=\left(\begin{array}{cc}ad& ae\\ bd& be\\ cd& ce\end{array}\right)$$

Multiplying matrices.

(M5-2)

$$\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)\times \left(\begin{array}{cc}e& f\\ g& h\end{array}\right)=\left(\begin{array}{cc}ae+bg& af+bh\\ ce+dg& cf+dh\end{array}\right)$$

Multiplying $2\times 2$ matrices.

(M5-3)

$$A\times A^{-1}=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$$

The identity matrix.

(M5-4)

$${\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)}^{-1}=\left(\begin{array}{cc}\frac{d}{ad-cb}& \frac{-b}{ad-cb}\\ \frac{-c}{ad-cb}& \frac{a}{ad-cb}\end{array}\right)$$

The inverse of a $2\times 2$ matrix.