Step 2To write the matrix in reduced row-echelon form, apply elementary row operations until we obtain zerosabove and below each of the leading 1's.First interchange the rows of the augmented matrix as given below.- 20 0 1:-1 11 115 10 20: 3416101.307Now perform the operation (-R1)on R1.(-글씨)-10 02-1 1101 11:30715 1020 : 3416Next, perform the operations (R2 + R1( ) on R3.on R2andR3 - R1-글 :-글 :10 0110(R2 + R1)→2(R3 - R1)→13075 1020 : 3416 A bank teller is counting the total amount of money in a cash drawer at the end of the shift. There is a total of$3416 in denominations of $1, $5, $10, and $20 bills. The total number of paper bills is 307. The number of$20 bills is twice the number of $1 bills, and the number of $5 bills is 10 more than the number of $1 bills.Write a system of linear equations to represent the situation. Then use matrices to find the number of eachdenomination.Step 1To find the equations for the given model, first define the variables as given below.x = number of $1 billsy = number of $5 billsz = number of $10 billsw = number of $20 billsAs per the given conditions, the system of linear equations will be as follows.+ 5y + 10z + 20w = 3416+ y +W =307- 2xW =-2.r- x+ y10Write the associated augmented matrix for the system.1 5 10 20 : 34161 11:307-20 01:-10 0 :10

Given: To determine: Matrix after operation

To write the matrix in reduced row-echelon form, apply elementary row operations until we obtain zeros above and below each of the leading 1's. First interchange the rows of the augmented matrix as given below. - 20 0 1 : - 1 1 0 0 1: 10 1 1 1 15 10 20 : 3416 307 Now perform the operation (-R1) (-R.)- 10 0 - -1 1 10 1: 307 20 : 3416 1 1 1 15 10 Next, perform the operations (R2 + R1) on R2 and R3 - R1) on R3. -글 : -글 : 1 0 0 0 1 10 (R2 + R1)→ (R3 - R1)→ 1. 1. : 307 1. 5 10 20 : 3416

To write the matrix in reduced row-echelon form, apply elementary row operations until we obtain zeros above and below each of the leading 1's. First interchange the rows of the augmented matrix as given below. - 20 0 1 : - 1 1 0 0 1: 10 1 1 1 15 10 20 : 3416 307 Now perform the operation (-R1) (-R.)- 10 0 - -1 1 10 1: 307 20 : 3416 1 1 1 15 10 Next, perform the operations (R2 + R1) on R2 and R3 - R1) on R3. -글 : -글 : 1 0 0 0 1 10 (R2 + R1)→ (R3 - R1)→ 1. 1. : 307 1. 5 10 20 : 3416

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Step 2
To write the matrix in reduced row-echelon form, apply elementary row operations until we obtain zeros
above and below each of the leading 1's.
First interchange the rows of the augmented matrix as given below.
- 20 0 1:
-1 1
1 1
15 10 20: 3416
10
1.
307
Now perform the operation (-R1)
on R1.
(-글씨)-
10 0
2
-1 1
10
1 1
1:
307
15 10
20 : 3416
Next, perform the operations (R2 + R1
( ) on R3.
on R2
and
R3 - R1
-글 :
-글 :
1
0 0
1
10
(R2 + R1)→
2
(R3 - R1)→
1
307
5 10
20 : 3416

A bank teller is counting the total amount of money in a cash drawer at the end of the shift. There is a total of
$3416 in denominations of $1, $5, $10, and $20 bills. The total number of paper bills is 307. The number of
$20 bills is twice the number of $1 bills, and the number of $5 bills is 10 more than the number of $1 bills.
Write a system of linear equations to represent the situation. Then use matrices to find the number of each
denomination.
Step 1
To find the equations for the given model, first define the variables as given below.
x = number of $1 bills
y = number of $5 bills
z = number of $10 bills
w = number of $20 bills
As per the given conditions, the system of linear equations will be as follows.
+ 5y + 10z + 20w = 3416
+ y +
W =
307
- 2x
W =
-2.r
- x
+ y
10
Write the associated augmented matrix for the system.
1 5 10 20 : 3416
1 1
1:
307
-2
0 0
1:
-1
0 0 :
10

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