REVIEWQ$2$ Write your answer for part $($b$)$ here.

$($c$)$ If we start with $50$USD,$35GBP,60$EUR,$200$INR, and $45$ CHF $,$ give the total amount converted to each of

the currencies. Feel free to use technology for the computation.

Total in USD:

Total in INR:

Total in GBP:

Total IN CHF:

Total in EUR:

d$)$ If vec$(b)=\left[\begin{array}{c}500\\ 500\\ 500\\ 500\\ 500\end{array}\right],$ explain why there won't be a solution to Avec$(x)=$vec$(b).$ You should be able to do this without doing

any computations. Think about what a solution would look like in the context of this problem.

$($e$)$ If vec$(b)=\left[\begin{array}{c}500\\ a\\ b\\ c\\ d\end{array}\right],$ and there is a solution to Avec$(x)=$vec$(b),$ what are the values of $a,b,c,d?$ What is vec$(x)?$ You can use

technology for row$-$reduction.

$($b$)$ If we have a bunch of money in the five different currencies, we might want to know how much it's worth in

a single currency. For example, if we have $30$USD,$10GBP,20$EUR,$150$INR and $20$ CHF $,$ if we convert

everything to USD, we'd have

$1*30+1\mathrm{.}3123*10+1\mathrm{.}1079*20+0\mathrm{.}0119*150+1\mathrm{.}1786*20$

or around $$90\mathrm{.}64.$

But what if we want to convert to another currency? Of course we could use another calculation like the one

above, but wouldn't it be great if we could do all the conversions at once? That would be great.

Give a $55$ matrix A such that if we multiply $A$ by a vector vec$(x)$ with the original amounts in the five currencies,

the resulting vector will give the total amount converted to each of the $5$ currencies. For example, if

vec$(x)=\left[\begin{array}{c}30\\ 10\\ 20\\ 150\\ 20\end{array}\right]$

$($which corresponds to the example above$),$ then when we compute Avec$(x),$ we should get a vector with $5$ numbers$-$

the first number should be the total in USD $(90\mathrm{.}64),$ the second should be the total in GBP$,$ and so on$.$

You can write your answer for $A$ on the next page.