At date t, the portfolio P to be hedged is a portfolio of Treasury bonds with various possible maturities. Its characteristics are as follows:

Price	YTM	Modified duration	Convexity
$28,296,919	8.511%	6.50	71.00

Consider the following Treasury bonds as hedging assets, with the following features:

Bond	Price($)	Coupon Rate	Maturity(yrs)
Bond 1	105.6540	4.00%	3
?Bond 2	101.2300	5.00%	7
?Bond 3	99.9850	6.00%	12

Coupon Frequency and compounding frequency are assumed to be annual. a) What is the number of hedging instruments necessary to implement a modified duration/convexity hedge?

b) Compute the YTM, modified duration and convexity of the three hedging assets.

c) what quantities of each of the hedging asset 1,2 and 3 would be necessary to hedge the portfolio P? The answerw is: a. We need three hedging instruments.

b. We obtain the following results:

Bond	YTM (%)	MD	Convexity
Bond 1	6.831	2.629	9.622
Bond 2	7.286	5.267	36.329
Bond 3	7.610	8.307	90.212

c. We then are looking for the quantities ?1, ?2 and ?3 of each hedging instrument 1, 2, 3 as solutions to the following linear system: ?1= ?279,536

?2= 290,043

?3=?379,432

I need help solving this problem? how should I do this?

1, P2 3 and 1, P2 3 and