# Math Help - Inverse of Matrixes

1. ## Inverse of Matrixes

An investment adviser has two mutual funds that she is recommending: a conservative bond fund with an assumed return of 3% a year and a stock fund with a projected return of 11% a year. One client has $29000 to invest and wishes a return of 4% per year, and a second client has$34000 to invest and wants a 8% annual return. How should the adviser allocate the money of each client between the bond fund and the stock fund?

The only thing I can't figure out is how to get this into 2 equations (ex: x+y = 5 form) to form a matrix so I can find the inverse. The rest I can do. Thanks.

2. Originally Posted by zweevu
An investment adviser has two mutual funds that she is recommending: a conservative bond fund with an assumed return of 3% a year and a stock fund with a projected return of 11% a year. One client has $29000 to invest and wishes a return of 4% per year, and a second client has$34000 to invest and wants a 8% annual return. How should the adviser allocate the money of each client between the bond fund and the stock fund?

The only thing I can't figure out is how to get this into 2 equations (ex: x+y = 5 form) to form a matrix so I can find the inverse. The rest I can do. Thanks.
There is insufficient information unless the investors require exactly the given returns, which is unlikely.

However assume that it is true. Look at the first investor, if they invest $\a$ in the bond and $\29000-\a$ in the stock the return is:

$\frac{0.04 \times a+0.11 \times (29000-a)}{29000}\times 100 \%=4\%$

which you solve for $a$.

CB