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need help with the assignment! didn't realize it was due in a couple of hours, ill send you all the notes we took in class thats needed to find these solutions

Math 110 Homework Assignment 3

due date: Oct. 7, 2016 1. List the different types of RREF possible for a 2 × 4 matrix (like we did in class for

a 2 × 3 matrix).

Bonus Question: How many different types of RREFs are there for a 2 × n matrix?

2. Put the following matrices into RREF.





3 2 1

(a)

6 5 4 2 ?6 ?1 6

(c) 4 ?12

2 20 3 ?9

0 12 (b)  10 6 9

15 9 12  ?1

6 ?1 ?1

(d) 3 ?18

1

0 2 ?12

3

0 3. For each of the following matrices (already in RREF) parameterize all the solutions

to the corresponding system of equations. Write your solution in vector form.

#

&quot;





1 ?4 0 ? 23 5

1 0 3 8

(b)

(a)

0 1 2 2

0

0 1

6 19 1 0 3 0 1 ?5

1 ?2 0 3 0 11 ?7

9 0 1 4 0

6 21 (c) 0 1 2 0 8

(d) 0

0 0 0 1 7

0

0 0 0 1 ?9 14

4

4. Pigeons are sold at a rate of 5 for 3 coins, swans at a rate of 7 for 5 coins, and

peacocks at the rate of 1 for 3 coins. A man was told to bring 100 birds costing 100

coins for the amusement of the King?s son. How many of each kind does he buy? (This

is a version of a problem from a 9th century Indian text.)

(a) If x is the number of pigeons, y the number of swans, and z the number of peacocks,

write down the corresponding linear equations and the augmented matrix for the

problem.

(b) Parameterize the solutions to the equations, where x, y, and z are real numbers.

(c) Finally, solve the problem of the riddle. Since x, y, and z are the numbers of

birds, they must be integers, greater than or equal to zero. Also, according to the

conditions of the problem, x must be a multiple of 5, and y a multiple of 7. There

is more than one solution; find them all. 1

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