I need help on matrices I don't understand

Question

A small business takes out loans from three banks to buy some new equipment. The total amount of the three loans is $34000. The first bank offered an interest rate of 16%. The second bank offered a rate of 18% and the amount borrowed from this bank was $5000 less than twice as much as the amount borrowed from the first bank. The third bank offered a rate of 15%. The total annual interest was $5650. How much did they borrow from each bank?(use matrice)

Answer 1

1              1             1             x             34000

0.16      0.18        0.15            y     =       5650

- 2           1              0             z            - 5000 

--------------------------                         ------------

                A                                             B

 

The third line of matrix A is obtained from y = 2x - 5000

or - 2x + y  + 0z = -5000

 

Let AI = inverse of matrix A.

Find AI. If you do not know how to do it manually, use a calculator to evaluate it.

Then multiply AI by B   = AI B to obtain the values for X, Y, Z.