Question 249949
I did NOT  use the inverse matrix method but all the info and equations you need should be here.

I=Prt
P=6500
I=560
t=1
r1=5%
r2=8%
r3=10%
P1+P2=P3-500
6500=P3-500+P3
3500=P3
P1+P2=3000
I=Prt
I3=3500*.10*1=350
I1+I2=560-350=210

.05 (P1)+.08(3000-P1)=210
1000=P1
P2=3000-P1=2000
so we have 
P1=1000
P2=2000
P3=3500
r1=5%
r2=8%
r3=10%
I1+I2=210
I3=350
I1 can be found by I=Prt
I2 can be found by I=Prt or 210-I1