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Math 18 MATLAB Assignment 2

Exercise 2.1 Cx= b x= [ 1.0714 1.2143

1.5714 ]

1. My solution is correct.

INPUT: >> x = C\d

OUTPUT: x =

1.0714 1.2143

1.5714

1. INPUT: >>C*x-d

OUTPUT: ans =

12.2143 9.2143 8.2143

11.5000 8.5000 7.5000

3.2857 0.2857 -0.7143

Exercise 2.2

INPUT: >> x= [-10 4; 15 -6]

OUTPUT: x =

-10 4

15 -6

INPUT: >> y=[0 0]

OUTPUT: y =

0 0

INPUT: >> h=x/y

OUTPUT: Warning: Rank deficient, rank = 0, tol = 0.000000e+00.

h =

0

0

My solution is the same. The error exists because the augmented matrix, h, is inconsistent because the last column contains a pivot.

Exercise 2.3

INPUT: >> rref ([C d])

OUTPUT: ans =

1 -3 2 0

0 0 0 0

0 0 0 0

There are 2 free variables.

Exercise 2.4

The columns all add up to one because each additive represents a percentage. 1 is 100 % and each row within the additive of 1 represents a factor of that 1. Exercise 2.5

The left-hand side of the equation coefficients are scalars of the variables f, t, c, m, and b. These coefficients represent A in the equation Ax=b. The variables f, t, c, m, and b are within the vector x in Ax=b, their letters represent the Farmer, Tailor, Carpenter, Miner, and Slack Bob respectively. Vector x also represents what these variable produce, Food, Clothes, Housing, Energy, and Alcohol respectively. Matrix A represents the percentage of consumption these variables of vector x represent. The right-hand side of the equation, b, represent the total price of each good of Food, Clothes, Housing, Energy, and Alcohol respectively.

Exercise 2.6

1. INPUT: >> x=C-I

INPUT: >> d=[0

0

0

0

0]

INPUT: y= [x d]

OUTPUT: y =

Columns 1 through 4

-0.7500 0.1500 0.2500

0.1800

0.1500 -0.7200 0.1800

0.1700

0.2200 0.1900 -0.7800

0.2200

0.2000 0.1500 0.2000

-0.7200

0.1800 0.2300 0.1500 0.1500

Columns 5 through 6

0.2000 0 0.0500 0 0.1000 0

0.1500 0

-0.5000 0 INPUT : >> rref([y])

OUTPUT:

ans = Columns 1 through 4

1.0000 0 0 0 0 1.0000 0 0

0 0 1.0000 0

0 0 0 1.0000

0 0 0 0

Columns 5 through 6

-0.8025 0

-0.5919 0

-0.7108 0

-0.7520 0

0 0

General Solution: p1=.8025b, p2=.5919b, p3= .7108b, p4=.7520, p5=free

The highest priced commodity is food and the lowest priced

1. commodity is clothes. Highest to Lowest Income: Farmer, Miner, Carpenter, Tailor, Slacker

Bob, in which Slacker Bob is a free variable. Slacker Bob has the highest income because the other occupations are just fractions of his income.

If Slacker Bob sells \$40,000 a year, the corresponding Gross incomes are true, Farmer=\$32100, Tailor=\$23676, Carpenter=\$28432, and Miner=\$30080.

Exercise 2.7

# a. INPUT: >> L=[0 1/4 1/4 1/4 1/4; 1/2

0 1/2 0 0; 0 1/2 0 0 1/2; 1/3 0 1/3 0

1/3; 0 0 1 0 0]

OUTPUT:

L =

Columns 1 through 4

0 0.2500 0.2500 0.2500

0.5000 0 0.5000 0

0 0.5000 0 0

0.3333 0 0.3333 0

0 0 1.0000 0

Column 5

0.2500

0

0.5000

0.3333

0

1. INPUT: >> j=L-I

OUTPUT: j =

Columns 1 through 3

-1.0000 0.2500 0.2500

0.5000 -1.0000 0.5000

0 0.5000 -1.0000

0.3333 0 0.3333

0 0 1.0000

Columns 4 through 5

0.2500 0.2500

0 0

0 0.5000

-1.0000 0.3333

0 -1.0000

INPUT: f =

0

0

0

0

0

INPUT: >> w= [j f]

OUTPUT: w = Columns 1 through 3

-1.0000 0.2500 0.2500

0.5000 -1.0000 0.5000

• 5000 -1.0000

0.3333 0 0.3333

• 0 0000

Columns 4 through 6

0.2500 0.2500 0

0 0 0

0 0.5000 0

-1.0000 0.3333 0

• -1.0000 0

INPUT: >> rref (w)

OUTPUT:

ans =

• 0 0 0 -1 0

0 1 0 0 -1 0

0 0 1 0 -1 0

0 0 0 1 -1 0

0 0 0 0 0 0

1. They all have equal PageRank because they all equal E. E is a free variable.
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