Let 2 a) Compute A and verify that A - 3A + 21 = 0. Deduce the Inverse of A. b) Find the inverse of A by the formula A = (Cofactor A)"/det (A).

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

A:

Q: appose that X1,X2, ... ,X, X)e = (1/2)(1+ X0); %3D how that 3X is a consis

A: The expectation of the distribution can be calculated as:

Q: Show that B is the inverse of A. 2 A = 1 1 %3D -1 -1 -1 -2 AB = %3D %3D %3D BA %3D

A:

Q: Prove that Eo 2i = 2n+1 – 1 - i3D0

A:

Q: 17. Given a = 4 – 4i and az = 4 + 3i, express %3D :11 in the form a + bi. a, az CLONE Dec 19

A:

Q: Prove that eax (a cos bx +b sin bx) + C. ax cos bxdx %3D a2 + b2

A: ∫eaxcosbxdx=eaxacosbx+bsinbxa2+b2+C

Q: 27 de Evaluate the intergal using the residue theorem. 15 +3 cos 0

A: residue theorem of integration

Q: Express each of the following in the form a + bi. cosh(1 – i2)

A:

Q: Show that the following gn are harmonic and find its conjugate u=3x^2y+2x^2_y^3_2y^2

A:

Q: Exercise 3: Solve the following equation for x and y where 3 xy – 2i + x + 2xyi – 5 = -- 3i 2

A: Solution of the equation

Q: Is w = zī harmonic ? if so find its conjugate.

A:

Q: 4) For A= a,āx + azay + a3az, B = b,ax + bzay + b3az, show that %3D %3D A.B cos 0 = A.AVB.B

A:

Q: If {an} and {bn} are divergent, then {anbn} is divergent.

A: Given; (an) and (bn) are divergent.

Q: = cos(x + y), when x = 0, y = " %3D

A:

Q: For a Cauchy-Euler DE the roots of auxiliary are m = -3 ± 3i then Ye = x (c, cos(3 In x)+ c2 sin(3…

A: Using substitution of Cauchy Euler D.E.

Q: tain the in

A: Given,             L-1s+2s2+6s+1=

Q: a) Show that fi (x) = x, f2(x) = cos 2x are orthogonal on

A:

Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

A:

Q: 4) For A = ajax + azāy + azaz , B = b,ax + b2ay + bzaz, show that A.B cos 0 = A.AVB.B

A:

Q: 1. dx %3D = cosx cos² t dt

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: D[Expf-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: Prove that t(Cos0-iSino)

A: To prove: 1z=1rcosθ-isinθ We know that polar from of complex number Z is defined as z=rcosθ+isinθ,…

Q: On taking AABC, use cosines law: 450 300 500 Om)* =(450 m)* +(500 m)* – 2×(450 m)(500 m ) cos A…

A:

Q: ez = -2

A:

Q: 1. Prove, with justification, that this equation is an identity: x + (a + b)r + ab (x+ a)(x + b).

A:

Q: Show that if v is a harmonic conjugate for u, then -u is a harmonic conjugate for v.

A:

Q: Show that cos A x e 2 *,x2 0. %3D

A:

Q: de Evaluate the intergal using the residue theorem. 13 +4 sin e

A:

Q: Prove that the calculate inverse is correct by using the formula I = A(A^(−1))

A:

Q: (b) Show that U (x, y) = eu cos v, V(x, y) = eusin v are conjugate harmonic of each other if f = u +…

A: It is given that,  f = u+iv  is analytic. We have to show that,  U(x, y) = eu cos v  and  V(x, y) =…

Q: Let 1 -1 1 A = -1 1 1 1 1 What is the cofactor C33?

A:

Q: + Cp"prove that If (1 + x)" = Co + Cx + Czr² + п(n + 1) 2 ... %3D C1 2C2 "Cn ... Co C1 Cn – 1

A:

Q: Show that the following gu are harmonic and find its conjugate U = 3x²³y + 2x² - y²³-2y²

A:

Q: Use the Euler , improved Euler and Runge-kutta nethoods to solve the following ODES : y - y tan x =…

A:

Q: de B: Evaluate the 2m a-cos20 when z = et and Iz| = 1. %3D

A:

Q: Exercise 3: Solve the following equation for x and y where 3 xy – 2i + x + 2xyi – 5 =- 3i | 2

A: This kind of problem we can solve by comparing the real and imaginary parts and after that solve the…

Q: Prove that Co +2C, +4C₂ +8C3 +..... +2 °C₁ = 3^

A: Given problem:- Prove that C0 +2C1+4C2+8C3+...... + 2n nCn =3n

Q: do Evaluate the intergal using the residue theorem. 12 +1 cos 0

A: ∫02πdθ12+1 cosθLet, z=eiθ . Then cosθ=(z+z-1)/2, dz=iz dθ, so that∫02πdθ12+1…

Q: 1 de, where a, b, and d are real and a² + b² < d² a cos e + bsin 0+d

A: The given integral is: ∫02π1acosθ+bsinθ+ddθ Also given that: a2+b2&lt;d2.

Q: Use the definition of limit complex function to find 8-e, for which lim(3z + 2) = 3i +2. O (A) 8=…

A:

Q: Express −i+j in the form [a,b]

A: Simplification

Q: If z = 3 – 3i, express 5/z  in the form a + bi

A: The given value of z is z=3-3i.

Q: Prove the followling identites 9) A-7-A 2. gn gntt

A: a) Given, ∆-∇=∆∇ Take LHS, ∆∇fx=∆∇fx Since, ∇fx=fx-fx-h ; Here h is the step size. and ∆fx=fx+h-fx

Q: 11. Assume that the stated inverses exist, prove (I+ A-B-)-A-1 = A-(I+B-1A-1)-1

A: We will use the properties of matrix multiplication to prove the given equality.

Q: Let A E R²x2 be special orthogonal. Show that there exists & E [0,27t) such that COS O - sin o A =…

A: According to question,Given Matrix,A = cos ϑ-sin ϑsin ϑcos ϑ

Q: Express Q(x) = cos4 (x )+ 12 as the composition of three func-tions; that is, identify f, g, and h…

A: Q(x) = cos4 (x )+ 12 We need to express the given function as a composition of three functions  that…

Q: Prove that the function w(z), expressing the roots of the equa- tion 3ర్ - 25w° + 60u - 2 = 0 in…

A: We consider z as a parameter and for each complex value of z will look for all complex roots w of…

Q: Evaluate (from 0 to pi) ∫(2sin(t)−1cos(t))dt

A:

Q: . Let z = x2 – x*y where x = r sin 0 and y = r cos 0. az and ae az Use the chain rule to find ar…

A:

Q: Show that, for any constants k' and 'a', u = sin(kx) sin(akt) is a solution of the equation Ut =…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.