Chapter 3.2, Problem 50E

Nutrition Suppose the weights (in grams) and lengths (in centimeters) of three groups of laboratory animals are given by matrix $A$, where column $1$ gives the lengths and each row corresponds to one group.

$A=\left[\begin{array}{cc}12.5& 250\\ 11.8& 215\\ 9.8& 190\end{array}\right]$

If the increase in both weight and length over the next 2 weeks in $20\%$ for group I, $7\%$ for group II, and $0\%$ for group III, then the increases in the measures during the 2 weeks can be found by computing $GA$, where

$G=\left[\begin{array}{ccc}0.20& 0& 0\\ 0& 0.07& 0\\ 0& 0& 0\end{array}\right]$

What are the increases in respective weights and measures at the end of these 2 weeks?

Find the matrix that gives the new weights and measures at the end of this period by computing

$\left(I+G\right)A$

Where $I$ is the $3\times 3$ identity matrix.