ECON 331 97/1
HOMEWORK ASSIGNMENT #2

The system of equations which represents the investor's problem is:

.75C             + .3E = 50  (invested in Canada)
.25C + .85U + .2E = 30  (invested in U.S.)
            .15U + .5E = 20  (invested in England)

In matrix form:
The coefficient matrix is:
> with(linalg):
> A:=matrix( 3, 3, [.75, 0, .3, .25, .85, .2, 0, .15, .5]);

                            [.75     0     .3]
                            [                ]
                       A := [.25    .85    .2]
                            [                ]
                            [ 0     .15    .5]

The vector of constants is:
> d:=vector( [50, 30, 20]);

                          d := [50, 30, 20]

The amounts to be invested in the three companies, C, U and E (a vector, x) is found by premultiplying the inverse of A with d:
> A_inv:=inverse(A);

                [1.284552846     .1463414634     -.8292682927]
                [                                            ]
       A_inv := [-.4065040650    1.219512195     -.2439024390]
                [                                            ]
                [.1219512195     -.3658536585    2.073170732 ]

> x:=evalm( A_inv &* d);

             x := [52.03252035, 11.38211382, 36.58536586]

