Solve q1 a) b) Ath Fundamental Methods of Mathem...Chapter 4 Lincar Models and Mutrix Algehra 69In Example 5, the square matrix A has nonzero elements a: and an in the principaldiagonal, and zeros everywhere else. Such a matrix is called a diagonal matrix. When adiagonal matrix A appears in the product x'Ax, the resulting product gives a "wcighted"sum of squares, the weights for the x and the x terms being supplied by the elements inthe diagonal of A. This result is in contrast to the scalar product x'x, which yictds a simple(unwcighted) sum of squares.Let the economic ideal be defined as the national-income level Y° coupled with the inflationrate p°. And suppose that we view any positive deviation of the actual income Y from Y° tobe equally undesirable as a negative deviation of the same magnitude, and similarly fordeviations of the actual inflation rate p from p. Then we may write a sociał-loss functionsuch asExample 6A = «(Y – Y©y² + B(p - pj?where a and B are the weights assigned to the two sources of social loss. If deviations of Yare considered to be the more serious type of loss, then a should exceed 8. Note that thesquaring of the deviations produces two effects. First, upon squaring, a positive deviationwill receive the same loss value as a negative deviation of the same numerical magnitude.Second, squaring causes the larger deviations to show up much more significantly in thesocial-loss measure than minor deviations. Such a social-loss function can be expressed, ifdesired, by the matrix productp- p)Matrix multiplication is aiso distributive.Distributive law A(B + C) = AB + AC(premultiplication by4](B+C)A = BA +CA[postmultiplication by 4]In each case, the conformability conditions for addition as well as for multiplication must,of course, be observed.EXERCISEverity1. Given A =B =and C =that(a) (A+ B) +C = A+(8 +C)(b) (A + B) – C = A+ (B – C)2 The subtDoes the commutative law of addition permit us to state that A - B = B – A? If not,how would you correct the statement?3. Test the associative law of multiplication with the following matrices:y ve conSIdered as the addition of the matrix (-1)B.-8 0 711 3 2A =B =C =070 Part Two Sutic for Equilihrium) Anulysis4. Prove that for any two scalars g and k(a) k(A + B) = k A + k B(b) (g+ k)A = gA + kA(Note: To prove a result, you cannot use specific examples.)5. For (a) through (d) find C = AB.[12 14][3 9]

Answered: RCISE 1. Given A = 2 E , verify that…

RCISE 1. Given A = 2 E , verify that (a) (A+ B) +C = A+(8 +C) (b) (A + B) – C = A+(B – C)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

Similar questions

es, Ted thinks that because 10 × 10 2 X 5 = 10, he should be able to calculate 12 × 15 by adding 100 + 10 to get 110. Explain to Ted in two different ways that, even though his method is not correct, his calculations can be part 9. 100 and of a correct way to calculate 12 X 15. a. by drawing an array b. by writing equations that use the distributive property
Determine : 2 4 3r -1? + 4t 9r - 21? +4t А.) O B.) 271 - 41? + 41 O c.) O D.)
Four students are working in a group and are asked to find the length of BC. Which two students set up the problem correctly? B Moe: x= V5 - 1)2+ (1 -4)2 4- Jimmy: = 32+ 42 Alice: x= 3 +4 -2- Jane: x= V5 - 1)² - (1 - 4)² AT A. Moe and Alice O C. Moe and Jimmy O B. Jimmy and Alice O D. Jane and Jimmy 中 P Type here to search BANG LOUTSEH 40 144 4+ 40 & %6 080 6
Solve the following equations for x: a) 2e6x 18 b) ex² =1 c) 2* = e5 d) 2*² = 5 e) lnx² = 5 In x f) Inx² - In 25 2 And solve the equation (x − 1)³ −x+1=0 hint: "Factor out" the term (x-1). Also, you should find three distinct solutions. 1)
4. Solve the quadratic equations using appropriate method. a) х? — х —30 %3 0 b) Зx? + 7х —7- 0 c) x? +8x – 9 = 0 d) x? + 8x +4 = 0 e) х? — Зх — 28 %3 0