Answer:
The answer is "rate 12%, 14%, 16% and value 4000, 10000, and 7000".
Step-by-step explanation:
Let the value is x, y, and z. so,
The value of x amount will be borrowed at 12% 
The value of y amount will be borrowed at 14%
The value of z amount will be borrowed at 16% 
If the total amount= 21000

If the total interest= 3000
calculating the total interest:

The overall amount borrowing at 12% and 14% was half as much as the amount borrowed at 16%.

by calculating the value we have 3 equations that are:

calculate the matrix by above-given value:
![\left[\begin{array}{ccc}1&1&1\\0.12&0.14&0.16\\1&1&-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%5C%5C0.12%260.14%260.16%5C%5C1%261%26-2%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{c}x&y&z\\ \end{array}\right] =\left[\begin{array}{c}21000&3000&0\\ \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%26y%26z%5C%5C%20%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D21000%263000%260%5C%5C%20%5Cend%7Barray%7D%5Cright%5D)
by solving the above matrix we get:
![\left[\begin{array}{c}x&y&z\\ \end{array}\right] =\left[\begin{array}{c}4000&10000&7000\\ \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%26y%26z%5C%5C%20%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4000%2610000%267000%5C%5C%20%5Cend%7Barray%7D%5Cright%5D)
