# A total amount of

Let the deposited be x, y and z respectively.

As per the Data we get,

x + y + z = 7000

5%x + 8%y + 8.5%z = 550

i.e 5x + 8y + 8.5z = 55000

x – y = 0

These three equations can be written as

A X = B

|A| = 1(0 + 8.5) – 1(0 – 8.5) + 1(– 5 – 8)

= 1(8.5) – 1(– 8.5) + 1(– 13)

= 8.5 + 8.5 – 13

= 4

Hence, the unique solution given by x = A – 1B

C11 = (– 1)1 + 1 (0 + 8.5) = 8.5

C12 = (– 1)1 + 2 (0 – 8.5) = 8.5

C13 = (– 1)1 + 3 (– 5 – 8) = – 13

C21 = (– 1)2 + 1 (0 + 1) = – 1

C22 = (– 1)2 + 2 (0 – 1) = – 1

C23 = (– 1)2 + 3 (– 1 – 1 ) = 2

C31 = (– 1)3 + 1 (8.5 – 8) = 0.5

C32 = (– 1)3 + 2 (8.5 – 5) = – 3.5

C33 = (– 1)3 + 3 (8 – 5) = 3

X = A – 1 B =

X =

X =

X =

=

Hence, x = 1125, y = 1125 and z = 4750

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