Answer:
- x = $6000 . . . . first year
- y = $10000
- z = $4000
- y = $8500 . . . . second year
- z = $7000
Explanation:
Given the set of equations related to investment, you want to know the values of x, y, z using the inverse of the coefficient matrix.
- x + y + z = 20000
- 0.08x +0.12y +0.20z = 2480 . . . second year: 2780
- -x +y = 4000
Inverse matrix
A suitable calculator or spreadsheet will tell you the inverse of the coefficient matrix. It is shown on the first line of the attachment. We have called it 'a'.
Solutions
The values of the variables x, y, z are listed in the columns of the last row of the attachment. We elected to solve both parts of the problem at once to save time and space. Each column of the constant matrix produces a corresponding column vector of the variable values when it is multiplied by the inverse matrix.
The solutions are summarized at the top of this answer.
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