Question

I need to make a matrix in reduced row echelon form

A real estate agency offers three apartments for rent in New Mexico City. The expected total revenue per month from monthly rentals for the three apartments is $1,600. The individual owners of these apartments bear the monthly maintenance costs of 20% of the rent for the first two apartments and 25% of the rent for the third apartment, which is a total amount of $345. The agency charges a monthly fee equal to 10% of the rent for apartments 1 and 3 and a fee equal to 20% of the rent for apartment 2. The monthly rent plus agency fees totals $1,820. Let x, y, and z represent the monthly rental for the first, second, and third apartments, respectively.

Answer 1

Just look at the picture lol

Explanation:

I took the quiz

Answer 2

Let the three apartments be A, B & C

The rent of A is $x

The rent of B is $y

The rent of C is $z

So x + y + z = 1600 .......(1)

Now

Maintenance of A is 20% of x = 0.20x

Maintenance of B is 20% of y = 0.20y

Maintenance of C is 25% of z = 0.25z

0.20x + 0.20y + 0.25z = 345

Multiplying by 100 we get

20x + 20y + 25 z = 34500

Dividing by 5 we get

4x + 4y + 5z = 6900 .......(2)

Monthly fee of A is 10% of x = 0.10x

Monthly fee of B is 20% of y = 0.20 y

Monthly Fee of C is 10% of z = 0.10z

Now

0.10x + 0.20y + 0.10 z= 1820 - 1600

0.10x + 0.20y + 0.10z = 220

Multiplying by 100 we get

10x + 20y + 10z = 22000

Dividing by 10

x + 2y + z = 2200 ....(3)

Making a Matrix of equation (1), (2) & (3)

`\left[\begin{array}{ccc}1&1&1\\4&4&5\\1&2&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right]  =\left[\begin{array}{c}1600\\6900\\2200\end{array}\right]`

is the required matrix