Refer to the mathematical model in Example 4:

(A) Does matrix equation (3) always have a solution for any constant matrix B?

(B) Do all these solutions make sense for the original problem? If not, give examples.

(C) If the total investment is k₁ = $10,000, describe all possible annual returns k₂.

Data from Example 4

An investment advisor currently has two types of investments available for clients: a conservative investment A that pays 5% per year and a higher risk investment B that pays 10% per year. Clients may divide their investments between the two to achieve any total return desired between 5% and 10%. However, the higher the desired return, the higher the risk. How should each client invest to achieve the indicated return?

Transcribed Image Text:

1 0.05 A 1 X L]=[] X1 k₁ 0.1 B (3)