(Solved): help solve 3.1 and 3.2 Problem 3.1 Consider the following matrices (some are row vectors, some are c ...

Problem $$3.1$$ Consider the following matrices (some are row vectors, some are column vectors): $$\mathbf{r}=\left[\begin{array}{llll}1& 3& ?2& 0\end{array}\right],\mathbf{s}=\left[\begin{array}{c}2\\ 0\\ 1\\ ?5\end{array}\right],\mathbf{u}=\left[\begin{array}{l}x\\ y\\ z\end{array}\right]$$ Calculate the following matrix products by hand. Show your work. a) $$rs$$ b) $$sr$$ c) $$ur$$ Problem $$3.2$$ For each of the following problems, indicate whether a solution to the problem would most naturally tend to include an IF statement (including IF/ELSE, IF/ELSEIF, etc.), a FOR loop, or a WHILE loop, and explain your reasoning. You may include more than one of the above structures, or none of the above, but explain your reasoning. a) Accept 50 position measurements $$x_i$$ and calculate the corresponding spring force $$F_i=k{x}_i+c$$ for each one. b) Simulate rolling a 6 -sided die 100 times. c) Ask the user to enter a number. Calculate the square root of that number. Print the square root to the screen. d) Ask the user to enter a number between 0 and 100. If they enter a number outside this range, display an error message and ask again. Repeat until they enter a number in this range, then perform some calculations with that number and display the result. e) Population growth can often be modelled using the logistic formula $$P_{\text{year }+1}?P_{\text{year }}\left[1+r\left(1?\frac{P_{\text{year }}}{K}\right)\right]$$ Estimate the number of years it will take a given population to reach 800 million by starting with the current population, repeatedly applying the formula, and stopping when $$P_{\text{year }}?8\times 10^8$$. f) Calculate and display the square root of $$x$$ if $$x$$ is not a negative number. Display an error message if it is negative.