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

Q: 1: Prove that (c a) * H = (c b) * H implies that a H = b H

A: Given an equation. We need to prove that : a*H = b*H where H is a subgroup of a group ( say G). Also…

Q: Given 21 = Z3 Prove jk 13 2.

A: Given,  ∠1≅∠3 To prove  j∥k

Q: What is eh REF of B? 1 2 1 1 B = نه who 1 0 -1 به T NC vсы N 5 0 2]

A:

Q: Given that en 2= V and en 3=W,express each of the fallowing in terms of vand w a) in zv0/3

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Q: b) Prove Y)- min (t, Ye, Kg) is a UMVUE of o non

A:

Q: 2 Let A | and U = H. Then A2017U is equal to = ... A) B

A:

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: 5. Prove that (Z, × Z6)/((2,3)) S Z12.

A:

Q: 6. Prove that if alb and k E Z, then a|(b+ ak).

A:

Q: (i),if i = j + 1)',if i = B = A-, if i +j mif i + j

A: Here we have to find the Matrix A and B then find the product according to the question, now the…

Q: 3 2 If A = use the Cayley-Hamilton theorem to determine A?. 5 1

A: We can solve this by using given information

Q: 5. Let z1 = a1 + b;i and z2 = az + bzi. (a) Find Im[z,Zz + (Z)? – 2,7 ]. (b) Prove that (z)² = z,² .

A: Rational Numbers: All the numbers which can be written in the form of pq. Here, p and q are integers…

Q: 3. Prove that {12a + 4b |a, b e Z} = {4c\c € Z}.

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 1. Given: m |l n, 2l = 23 Prove: a | b 21 3 Proof:

A:

Q: 2. Suppose A is an m x n matrir, x ɛ Rª and Ax = b. Then b is in 1) R" | 2) R™ 3) RmfnT 4) R™n

A: Given :  A is an mxn matrix , x∈Rn and Ax=b   To find :  b is in which space of the given spaces.

Q: 4. Given that AB || CF, m²E = 48 ° and mZB=78°, Prove: mzF=30° %3D A. C. 789 48

A: We will solve it by using properties of angles

Q: 1. Prove the following in SDE. P+ Q, Q→ R, R→ S - P –→ (R A S)

A: When we infer a conclusion from a given premises in order to produce an argument, we use laws of…

Q: Hi, parts a) and b) of this question are attached.    Thanks so much!!!

A: For (a),

Q: 5. Prove that if A and B are similar then dim(ker(A)) = dim(ker(B)).

A: We have to prove dim(ker(A)) = dim(ker(B)).

Q: Prove that ifx > 3 and y> 4, then xy > 11.

A:

Q: 4 Let X,) be a pankizlly oadered e For x,y € X deftre xLy eff x sy and x#y. Pucose the Fallowiag:…

A:

Q: Prove that if n> m - 1, then J,(x) = 2(x/2)"-m

A:

Q: 27) Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC 0 6 71 ΓΟ 1 1] 2 If A = -6 0…

A:

Q: Prove that if r>3 and y > 4, then ry > 11.

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: Show that for n, m e Z+, gcd(2" – 1,2m – 1) = 2gcd(n,m) – 1.

A:

Q: 3. Suppose a, b, c E Z. Prove that if a? + b = c²,, then a is even or b is even.

A:

Q: 44. (a) Let a, b, ceZ with (a, b) = 1 and a | bc. Prove that a c. (b) Provide a counterexample to…

A:

Q: Let x, y, A, u E Z. Prove that if 1 = Ax + µy then r, y are relatively prime.

A:

Q: Let a e Z. Prove that if 7 | 2a, then 7 | a.

A:

Q: Prove that if A is similar to B and B is similar to C, then A is similar to C.

A:

Q: 1. Let z E C. Prove that Re(z?) = [Re(z)]? - [Im(2)]² and Im(z²) = 2 Re(2) Im(2)

A:

Q: 3. Let A = {3k : k € Z} and B = {15m + 12n : m, n € Z}. Prove that A = B.

A: Let     A = {3k : k∈ℤ}    and          B = {15m+12n: m,n∈ℤ}To show :- A=B∵Let  x∈B  ⇒x = 15m1+12n1…

Q: (a) Given that x= In2 and y = In 5, (i) express In 50 in terms of x and y,

A: Simple logarithm problem.....

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: Prove the given statement by the indicated method. (1). By Direct Proof: "Vm,n € Z*,+> 2."

A: ∀m, n∈ℤ+,We know square of an integer is always non-negative Hence (m-n)2≥0…

Q: 9. Prove or disprove. (a) Vn e Z*, n² < 2". (b) Vm e Z, if m is odd, then m² is odd.

A: In this question we have prove if this equation are valid or not.

Q: 10.B.4: Suppose TE£(V) andcEF. Prove that det (cT) = cdim V det T.

A: Here given that T∈L(V),is the set of linear maps from V to V.

Q: 4.2. Let a, b E Z, where a 0 and b 0. Prove that if alb and bla, then a = b or a = -b. -b.

A:

Q: 53. Suppose that a + 0. (a) If a · b = a·c, does it follow that b (b) If a X b = a X c, does it…

A: Given a, b, c are three vectors and a ≠ 0.

Q: 4|5" – 1, Vn e N

A:

Q: Prove: Vn e Z,if n is odd, then 3n+5 is even.

A: Consider the provided question, To prove: if n is odd integer, then 3n + 5 is even. Proof by…

Q: Prove the following using resolution refutation: 4. Given: (p Aq) -→r, p^ s A~w, (s A t) →q, tv w…

A: Given 4 premises p∧q→r, p∧s∧~w, s∧t→q, t∨w. The conclusion to be proved is r. We know that a…

Q: 4.2. Let a, b € Z, where a + 0 and b + 0. Prove that if alb and bla, then a = b or a = -b.

A:

Q: c) Compute µr, Hy, Ož, o, Cov(X, Y), and p

A: Reviewing information, Given pdf is, f(x,y)=x+y                 ; 0≤x≤1 ,  0≤y≤1

Q: By using Caushy Rieman prove that (2) and (3) (2) 4ca) = e (3) .w prove Thot()-

A: (a)

Q: Under what conditions on A and B is (AB)-1 = A-1B-1? Prove your assertion

A: Assertion: If A and B are commutative, then  AB-1= A-1B-1.

Q: Prove that if c=12n+4 where n in Z then c is not a linear combination of 27 and 18

A:

Q: Q1: Prove that ; If CE AB, D E AB and C# D, then CD = 2 %3D

A: Key point: 1. There is only one line possible from two distinct points.2. The line is expressed in…

Q: 3.1 Prove: For all a and B in R, Ja + B] > | |a| – |B||. Hint: la + B] = |a – (-B)|-

A: Answer is in below steps.

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.