Dalia inherited $15,000.00 and invested part of it in a money market account, part in municipal bonds, and part in a mutual fund. After 1 year, she received a total of $730.00 in simple interest from the 3 investments.

The money market account paid 4% annually, the bonds paid 5% annually, and mutually funds paid 6% annually. There was $2,000.00 more invested in the mutual fund than in bonds. Find the amount that Dalia invested in each category using any matrix method you know.

x = amount in money market

y = amount in municipal bonds

z = amount in mutual fund

x + y + z = 15000

4x + 5y + 6z = 73000

z = y + 2000 => 0x - y + z = 2000

Let’s create an Augmented Matrix and perform Row Operations on it to change it to a Reduced Row Echelon Form; from which we get the answers.

R1 1, 1, 1, 15000

R2 4, 5, 6, 73000

R3 0, -1, 1, 2000

R1 > R1 + R3

R2 > R2 - 4*R1

R1 1, 0, 2, 17000

R2 0, 5, -2, 5000

R3 0, -1, 1, 2000

R2 > R2 + 5*R3

R1 1, 0, 2, 17000

R2 0, 0, 3, 15000

R3 0, -1, 1, 2000

R2 > R2/3

R3 > -R3

R1 1, 0, 2, 17000

R2 0, 0, 1, 5000

R3 0, 1, -1, -2000

R1 > R1 - 2*R2

R3 > R3 + R2

R1 1, 0, 0, 7000

R2 0, 0, 1, 5000

R3 0, 1, 0, 3000

Swap R2 & R3 [optional]

R1 1, 0, 0, 7000

R2 0, 1, 0, 3000

R3 0, 0, 1, 5000

Solution: ($7000,$3000,$5000)

check:

(7000) + (3000) + (5000) =? 15000

15000 = 15000 √

4(7000) + 5(3000) + 6(5000) =? 73000

28000 + 15000 + 30000 = 73000 √

- (3000) + (5000) =? 2000

-3000 + 5000 = 2000 √