ECON 337 Quiz: Finding Inverses of 3 by 3 matrices

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purpletiger335

7 Nov 2016

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For any entry the minor is the 2-by-2 determinant formed by deleting the row and column of the entry in question. 5 the minor for the entry 2 is. 47 and the minor for the entry 1 is. The matrix of cofactors is found by changing every second sign in the matrix of minors. For the example, the matrix of cofactors is. The adjoint is the matrix of cofactors transposed. When the original matrix is multiplied by the adjoint, the result will look like. If the determinant is zero, the original matrix is said to be non- invertible, or singular. If the determinant is not zero, then the inverse of the original matrix is. Remember that for symmetric matrices you get a lot of free ones. Find the inverses and determinants of the following matrices: Use the inverses of 1d) and 1e) to solve the following systems:

Related Questions

PROBLEM SET ONE -2 - PRICE-ELASTICITY OF DEMAND

	P₁	P₂	Q_D1	Q_D2	I	II	III	IV	V
1	1	2	10	5
2	5	3	40	90
3	12	20	200	200
4	3	2	9	9
5	0.40	1.40	30	15
6	1.2	4.0	20	15
7	7.5	4.6	40	30
8	5	5.000â¦01	1x10⁶	0
9	5	4.9999â¦.	10	1x10⁹
10	6	12	12	6
11	18	36	360	180
12	7	15	24	16
13	7	16	78	78
14	25	65	150	100
15	65	91	1300	780
16	4	5	21	11
17	8	4	30	54
18	140	275	625	495
19	78	91	780	780
20	91	78	780	780

Column I - determine the Price-Elasticity of Demand Coefficient. Find material in Chapter 6 and the Powerpoint of Elasticity Chap 004 19e.ppt

change in quantity demanded change in price

E_D = ---------------------------------------- â ----------------------------

sum of quantities demanded / 2 sum of prices / 2

The data in the first four columns represent price (P) and quantity demanded (Qd) in time 1 (before change in price) and time 2 (after change in price). Note that results should be expressed in absolute terms (see paragraph Elimination of Minus Sign). For example, -1 should be expressed as â1â.

Column II â Based on topic concerning Interpretations of E_D, indicate which applies based on how the quantity demanded changed subsequent to a change in price (elastic, inelastic, etc.)

Column III - you need to determine if the good in question would be considered a necessity, a luxury or neither.

Column IV â Indicate, in monetary terms, how much is the change in total revenue or total expenditure (TR = P X Q_D), from the first price level to the second.

Column V - the direction of the change, also in monetary terms, that is, increasing or decreasing, and by how much? (show a + sign for increasing and a â sign for decreasing).

Note: for any monetary result please include the applicable currency symbol ($, â¬, etc.)

salmoneagle868

Labor Output Price (D1) Price (D2)

0	0	10.00	10.00
1	15	10.00	9.50
2	29	10.00	9.00
3	42	10.00	8.50
4	54	10.00	7.50
5	65	10.00	6.50
6	75	10.00	5.50

1. Suppose the firm's product demand is given by the column labelled D1. If the wage rate is $100, the firm will achieve maximum profit by hiring _____ workers.

a. 3 b. 4 c. 5 d. 6

2. Suppose the firm's product demand is given by the column labelled D1. If the wage rate rises from $100 to $130, the firm will reduce the quantity of labour employed by _____ unit(s)

a. 0 b. 1 c. 2 d. 3 16.

3.Suppose the firm's product demand is given by the column labelled D1. If the wage rate is $120, the firm will achieve maximum profit by hiring _____ workers.

a. 3 b. 4 c. 5 d. 6 3 17.

4. Suppose the firm's product demand is given by the column labelled D1. The value of the marginal product of the fourth worker is:

a. $10 b. $54 c. $120 d. $540 18.

5. Suppose the firm's product demand is given by the column labelled D2. If the wage rate is $100, the firm will achieve maximum profit by hiring _____ workers

a. 2 b. 3 c. 4 d. 5 19.

6. Suppose the firm's product demand is given by the column labelled D2. The extra revenue generated by the fourth worker is:

a. $1 b. $12 c. $48 d. $405 20.

7. Suppose the firm's product demand is given by the column labelled D2. If the wage rate rises from $100 to $130, the firm will reduce the quantity of labour employed by _____ unit(s).

a. 0 b. 1 c. 2 d. 3 21.

8. Compared to a firm facing D1, a firm facing demand schedule D2 but paying the same wage will hire:

a. the same number of workers, since the total product is the same in both instances

b. fewer workers, since product price declines as output increases

c. more workers, since product price declines as output increases

d. more information is required

blushkoala457

Emmanuel enjoys growing zucchini in his garden and then selling his produce at the local farmers' market. The table below shows his marginal benefit and marginal cost for each hour he spends in his garden per week. The figure below plots the marginal benefit and marginal cost points.

Emmanuel's Marginal Benefit and Marginal Cost of Gardening
Hours Spent Gardening	Marginal Benefit (dollars)	Marginal Cost (dollars)
1	$21	$3
2	18	6
3	15	9
4	12	12
5	9	15
6	6	18
7	3	21

a. Given the information above, what is Emmanuel's optimal amount of time spent gardening each week?

1 hour
4 hours
0 hours
7 hours

b. If Emmanuel were to spend 2 hours each week gardening:

marginal cost would exceed marginal benefit by $12.
marginal benefit would exceed marginal cost by $12.
marginal benefit would equal marginal cost.
marginal benefit would exceed marginal cost by $18.

c. If Emmanuel were to spend 6 hours each week gardening:

marginal cost would exceed marginal benefit by $12.
marginal benefit would exceed marginal cost by $18.
marginal benefit would exceed marginal cost by $12.
marginal benefit would equal marginal cost.

ceruleanoyster72

ECON 337 Quiz: Finding Inverses of 3 by 3 matrices

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