A bank teller is counting the total amount of money in a cash register at the end of the day. There is a total of $2600 in denominations of $1, $5, $10 and $20 dollar bills.

The total number of paper bills is $235. The number of twenty dollar bills is twice the number of $1 dollar bills and the number of $5 dollar bills is ten more than the number of $1 dollar bills. What is the system of equations to represent the situation. Then use matrices to find the number of bills for each denomination.

X $1 Bills.

2x $20 Bills.
(X+10) $5 Bills.
Y $10 Bills.

x + 2x + (x+10) + y = 235
4x + 10 + y = 235
Eq1: 4x + y = 225.

1*x + 20*2x + 5(x+10) + 10y = $2600.
46x+50+10y = 2600.
Eq2: 46x+10y = 2550

-40x - 10y = -2250
46x + 10y = 2550
6x = 300.
X = 50.
2X = 100
X+10 = 60

4*50 + y = 225
Y = 25.

The student should solve Eq1 and Eq2 using matrix and get the same results.

Let's define the variables:

Let x represent the number of $1 dollar bills.
Let y represent the number of $5 dollar bills.
Let z represent the number of $10 dollar bills.
Let w represent the number of $20 dollar bills.

Now let's analyze the given information:
1) The total number of bills: The total number of paper bills is 235. This means that the sum of the number of $1, $5, $10, and $20 dollar bills should equal 235.
x + y + z + w = 235

2) The number of twenty dollar bills: The number of $20 dollar bills is twice the number of $1 dollar bills. Therefore, we have:
w = 2x

3) The number of five dollar bills: The number of $5 dollar bills is ten more than the number of $1 dollar bills. We can express this as:
y = x + 10

We now have our system of equations:
x + y + z + w = 235
w = 2x
y = x + 10

To use matrices to solve this system of equations, we need to represent the system in matrix form as follows:

1 1 1 1 | 235
0 0 0 1 | 2x
0 1 0 0 | x+10

Now we can solve this system using row operations to find the value of each variable.