3. Let A, BE M2(Z3) be given by [1 2] B 0 2 A = 1 Find AB, BA, and A? (recall that A2 = AA).

Q: For which values of a and m does ax = 1 have a solution in Zm?

A: Claim:

Q: 12 3. If u lx + my, v = mx-ly, show that ди 4 + m

A:

Q: 2. Solve the following Cauchy problem: Uu = Uzz -0 0, u(x,0) = x – a², u(x,0) = 4x, -00 <x < 0. %3D

A:

Q: =[12] and U- = -[] Then A2017U is equal to -1 Let A =

A:

Q: Let x, y, z E R. Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

A:

Q: Suppose E(X) = 1, V(X) = 2, E(Y)= 3, V(Y) = 4, and E(XY)= 5. (1) Сov (X, Y) (2) Corr(X,Y) (3)…

A: 1) COV(X,Y) =E(XY)-E(X)E(Y)                    = 5-1×3                    = 2

Q: 5. Show that if x,y∈Z and 3|x^2+y^2 then          3|x or 3|y 6. Show that if c=sa+tb where c=(a,b),…

A: Please check that x=1,y=3, then x^2+y^2=10 does not divide by 3. So  must 3|x and 3|y instead of 3|x…

Q: 28x+4y+kz -10 -5x-8y-4z = -2 e must have, k +|

A: The given system of equation is: - 6x + 4y + 7z = 3 28x + 4y  + kz = -10 - 5x - 8y - 4z = -2

Q: Consider a, = V4n² + 3n – 2n for n > 1. %3D -

A: Introduction: The sequence is a set of functions with the set of natural numbers as the domain of…

Q: 46. Let the assumed particular solution for the given DE be y, = (Ar³ + Bx² + Cx)e* + E. What is the…

A: A detailed solution is given below.

Q: Since D is a square whose vertices have coordinates (0,0), (0,1), (1,0) and (1,1), which of the…

A: Please refer to the image below

Q: 17. AABC - AXYZ (not shown). If AB = 5, BC = 8, XY = y, and YZ= 2y – 3, find y. 17. y = P Type here…

A: We have to find y from the given information

Q: 10- Solve the problem: Utt-4uxx = xt, 00 u(x,0) = x, 4(x,0) = 0, u(0, t) = 0, Ux(1,t) = 1+t, t20 %3D

A: Given, utt-4uxx=xt;   0&lt;x&lt;1, t&gt;0 ⋯⋯⋯⋯1ux,0=x,   utx,0=0,   0≤x≤1,⋯⋯2u0,t=0,   ux1,t=1+t,…

Q: 1 If z = 2 V3 -i, then find ()*

A: Given complex number is: z=-1-3i2 Find the conjugate of complex number: z¯=-1+3i2 Find z¯4?

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

A:

Q: 2. Find p and q such that |5x - 2| ≤4 implies Ps 23x-4 5 ≤q.

A: Given |5x-2|≤4

Q: 2. The exact value of sec 57 is O2 2V3 -2 2V3 3

A:

Q: 1 Show that xn-m)}-2X(2). assu me. Zera 1c

A: As per the company's rule, we are supposed to solve one problem or three subparts. As there are two…

Q: Consider the following model: Y = Bo + B1 + U4, where u = 4+4-2

A: Given information: The auto regressive model is given.

Q: /et A 3 8 カー (-45 Show That LA+B S ZA+B) 3-5 = At B

A: Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given…

Q: 4 16 Define T: R? - R° by T(x) = Ax, where A = 1 3 -

A:

Q: 2. A firm produces two goods in pure ompetition &amp; has the pllowing TR &amp; TC functions R= 15Q…

A: In this question, concept of optimization is applied. Optimization Mathematical optimization is the…

Q: 42. Show that S 4xys + %3D 1- x2 1- y? 1– 22 (1 – a²) (1 – 3²) (1 – 2²) if xy + xx yz = 1

A: Given that  xy+yz+xx=1 Prove that the expression

Q: 5. (BH) Calculate det B, where 0. 4 1 1 В — 1 -2 4 -1 2 1 -1 0 7

A:

Q: c) If det (M) = 2 and det(N) = 3, calculate: %3D %3D i det (NM-'N). 1 ii det (M©N*(M-1)^(N-1)³).

A: Given that, detM=2 and detN=3. Results Used: detAB=detAdetB detA-1=1detA detAn=detAn (i) To…

Q: 1. Is the following always true? If yes, clearly explain why. If no, give a specific counterexample…

A: Note: AS per our guideline we are supposed to answer only one question. Kindly repost the other…

Q: a) Let Z = 7 – 13i, find: i) Im ) ii) (Re Z)?

A: Complex Numbers: The complex number is basically the combination of a real number and an imaginary…

Q: If A is a 2 x 2 with det(A) = 3, then det(4A1) = %3D

A: det(A-1)=1det(A) det(4A-1)=4ndet(A-1) where n is the order of the matrix.

Q: If A, B are 3 x 3 matric det(AB ') = 12 and a Then det(3A". (B)¯1)

A:

Q: 1. Let s, =2+j8 md -, = 4+j36. Show that a. -1+- = -+- 1 -1- -2 -1 -2 = -1-2 -1 : b. C d. =2 ||

A:

Q: 21. Find af and of if f(x,4)= 3x" +2xy+ Sy , x= 4v? + Bn", and u 2v-w? Vour %3D 4= 2v-w? Vour av…

A: We have to check

Q: 13- dy + 2xy = y diferansiyel denkleminin genel çözümü aşağıdakilerden hangisidir? -x* +c1 y = e a)…

A:

Q: 1. Lat A - [; : - and B = 2 2 1 3 4 (a) Compute AB. (b) Compute BA.

A:

Q: 10 Consider A :3D and y:= Find all re R that minimize || Ar - y|l2.

A:

Q: For which values of a and m does ax = 1 have a solutionin Z m?

A: To find for which values of a and m does ax=1 have a solution in Zm. Zm=0,1,2,....,m-1 when a=0,…

Q: 6. Prove that, if a, b e Z, then 3a? – 4b – 5 0. - -

A: Answer

Q: (b) Let z = x + iy = re?". Find |z| and z² first in terms of x and y and then in terms of r and 0.…

A: Given:

Q: al solution of - uy = 0 is O is *+c,e¯*)(c

A:

Q: 1),Given: AB || CD; AC 1CD Find: x and y A, ax ay by 4,

A: Here given as Given  CD||AB Also given ∠ACD=90Then∠CAB=909x=90⇒x=10

Q: 4 Ruret MC w co , , d, 7 the y a Fid e co f de

A:

Q: The set of solutions to z^6=−i is?

A: We have to find The set of solutions to z^6=−i.

Q: 9.12 suppose; a 3. A. %3D bる 19. .bz .(3. olet (A) = 2.. assume that fhe de teminanf ef find this…

A: We have to find determinant

Q: Let z=xin(x2+y²-eª)-162xy, x=te°, y=et. If the value of when s=2 and t=1 is equal to Ae?+Be", then…

A:

Q: 2. 1. If UZ = x+ 21 and ZS = 3x – 15, find US.

A:

Q: 17- (* +)dz + 2rydy -0 diferansiyel denklemi homojen olduğuna göre k değeri aşağıdakilerden…

A:

Q: Write equation for each ellipse

A:

Q: D B. E C Given: AB XEB = CB × DB Prove: AABC- ADBE

A: To Determine: prove △ABC~△DBE Given: we have a figure in which we have triangles △ABC and △DBE also…

Q: 16 3. Show that for x2 + 2xy - 3y² = 4, y" (x-3y)3

A: We will find y" as following.