Q2: if A= [{1,2},{3}], H= [{1}, {2,3}], G= [{1,3}, {2}] Show that A, H and G are mutually disjoint

Q: 27 Find (all) the value(s) of c such that 3c 3can - 8. n=0 (A) c= 3 (B) с%3D 4 (C) c = -}, (D) c = }…

A:

Q: Q3- Find the numerical value of g. xdz, if c = c + C2 + C3.defined in the given figure. (2,2) C3 C2…

A:

Q: (a) Find x, y for the following

A:

Q: 26) If x, y, u, v are variables connected by the relations 1 1 x? =au? +bv2, y² =au² –bv² where a…

A: Given, x2=au12+bv12…1y2=au12-bv12…2 Equation 1+2 gives:…

Q: Let i = i +2j+3k , Find e so that ||c|| = 3.

A: As we know that; The property of scalar multiplication of a vector ka→=ka→ Given: u→=i→+2j→+3k→

Q: Given that z, -[3,0.7], 2₂ [2, 1.2] and z, -[4,-0.5], (a) find z, xz₂ and 2₁ x 23 (b) show that [1,…

A: Given: z1=3, 0.7 ; z2=2,1.2; z3=4, -0.5 find a) z1×z2 and z1×z3 b) Show that 1,0×z1=z1 We know that,…

Q: Let a=3i-2j, b=-i+4j, r=7i-8j. If r=ka+mb, then k+m=... 1. O -1 2. O 2 3. О 1 4. O 3

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: Let ā = and b . Find 3ā + b. -

A: We will simply use vector addition rules to find the answer

Q: Let  A = (1 1 1, 1 2 2) Find R(A), R(AT), and N(A)

A: Given,A=111122the reduced row echelon form of AMake zeros in column 1 except the entry at row 1,…

Q: Given u(x, t) = t-²e¯, 2 , compute:

A: We can find the required answer as below.

Q: Let A & M and μ*(A) < oo. st B₁, B2,..., BEC, k <co with Bin B „²(AAŬB₂) <« j=1 any two sets E₁ and…

A:

Q: 4. Show that for all formulas p, p,0 E S(P), (a) (9 = 4) = ¬(4 ^ ¬ab).

A:

Q: b, c e R such that abc

A:

Q: In the figure shown, CF intersects AD and EH at points B and F, respectively. B G Complete the proof…

A: To complete the proof

Q: Let A = {x E R : 2 < x < 3} and B = {r €R: -1<r< 2}. Prove that |A| = |B|.

A: To prove this result we first show a objective map from [-1,2] to [2,3]. Then (2,3) is uncountable…

Q: It gER[a,b] and if h(x)=q(x) except for a finite number of points in [ab],then prove that he R[ab]…

A: The continuous set of [a,b] should be divided into finite sets first.

Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

A:

Q: If z1 = 1+ jb , Z2 = re¬1² , z/z2 = -10 , determine all possible values of b and r %3D

A:

Q: Q1) If B = B-1 then B = I or B = -I. Prove or give counter example. %3D

A: A detailed solution is given below.

Q: For what value of k,the points (k,k),(2,3) and(4,-1) are collinear.

A:

Q: АР 1. Find the point P such that - АВ = r, where A(4,3, –2), B(-5,0,4) and r = NIM

A: As per bartleby guidelines, I can answer only one question. So, please repost the other two…

Q: Show that e = (1 + i)/√2 if and only if z = (n/4+2km)i, k = 0.±1, +2...

A: This question is related to complex numbers,  we will solve it using given information.

Q: Given that Z - N (0,1), find k if P(\Z| < k) = 0.8. %3D O 1.282 O -0.253 O 0.842 O -4.5

A: We have given that  Standard normal i.e, Z~N(0, 1).

Q: Find all numbers z such that Az + Bz² + Cz = D [2 4 21 li 3 B=[i 1 1. A = -2 -1 [2 4 2] C = 1 3 1 -1…

A: Find all numbers z such that Az3 + Bz2 + Cz =D Given matrices,                              A=242131…

Q: the convolution theorem) e" dr re" (b) С (d) L{ / rsin(r) dr re" dr

A:

Q: (a) Prove that de 2n a>b>0 Jo a+ bcose Ja? - b2

A: We will use basic knowledge of Integral Calculus and trigonometric identities to solve this…

Q: 4. Let A %3D {a, b, c}, В %3D {x, у}, and C %3D {0, 1}. Find a) АхВх С b) СхВхА с) СхАх В d) ВxВxВ.

A: Given that: 4. A={a, b, c}, B={x, y}, C={0, 1}   NOTE: As per our answering guidelines, we can only…

Q: If w=f(p, q, r), where p-z2-y², q=y²-22, and r = 22-2², show that 1 Ow x 8x + 1 8w у ду + 18w z Əz…

A: Given w=f(p,q,r)and p=x2-y2,   q=y2-z2 and r=z2-x2

Q: If X ∼ N (μX , σ2X ) and Y ∼ N (μY , σ2Y ) are independent, then prove X + Y ∼ N (μX + μY , σ2X +…

A: X~Nμx,σx2 and Y~Nμy,σy2 are independent. Here, X~Nμx,σx2. In this context, it is known that the…

Q: V and for all r € R. Show that (V, 1

A:

Q: 5,t2 %3D as t= 5, 1, = 8. Find t

A: The nth term of the Arithmetic sequence is given by tn Therefore tn=t1+n-1d where t1is the first…

Q: a) If Z1 = -3 + 3i and Z2 = 4i. Show that: i) Arg(Z,Z2) + Arg(Z,) + Arg(Z2) ii) Arg (2) = Arg(Z,) –…

A:

Q: 7- Find a given that A(0, a)is equidistant from P(3, -3) and Q(-2,2).

A:

Q: Q2/ prove [A] [A] = [I] if [2 4 -5 [A]= 2 7 1 3 4

A:

Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j

Q: Find (t), given 7(t) = (- 2 In(5t), - 5/5t, – et). %3D F'(t) =

A: Explanation of the solution is given below...

Q: a- If A = -1 %3D 2 and B = -41 prove that (A + B)T = AT + B". 12 [1/2 - If A-1 =1/2 -1/2) and |A| =…

A:

Q: Determine whether A and B are independent, positively associated or negatively associated in each of…

A:

Q: 3 Reverse the order of whyndien of ? X (6x-2) dyds x- 4

A:

Q: Let x~ N( M, -) Ti- 5, Ź (xi-x)* 2 %3D %3D n -1 Ź(xi- 7)" 2 2. T2 = 2. 2. 2. Check the Consist of 6,…

A: We know that, Y=∑xi-x¯2σ2~χn-12 Then  EY=n-1⇒E∑xi-x¯2σ2=n-1⇒E∑xi-x¯2=n-1σ2---&gt;1…

Q: ALMN has vertices L(-2, 2). M(2, 3) and N(2, 0) L.

A: Coordinates of L = (-2,4) Coordinates of M = (6,-2) In right angle triangle circumcentre is the mid…

Q: 2. Let A € M, (R) be given. (a) If AA = 0n, prove that A = 0₁. Does this hold if A € M₂, (C)? (b)…

A:

Q: Then prove that 3 (i) P (AUB) > 1 (ii) <P (An B) S 10

A: Answer: From the given data, P(A) = 3/5 and P(B) = 1/2

Q: Which of the following is a fundamental set of solutions of y" + 6y' + 5y-0? a) O {e', e} b) {e,3e}…

A: The given differential equation is a second-order homogenous linear differential equation. First,…

Q: ii) Given Z, = -1 + iv3 and Z, = -v3 + i, show that In (Z,.Z2) # InZ, + InZ2

A:

Q: Given uo, u1, U2, U3, U4 and ug and assuming the fifth order differences to be constant, prove that…

A:

Q: a b be suc b |, then t

A:

Q: P.15.25 If A E M, is symmetric, prove that AT is symmetric.

A: