Is it true that the rank of [B AB If not, under what condition will it be true? A"-B] equals the rank of [AB A²B A"B]? ... ...

Q: 3. Prove that (An B)² C A × B.

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Q: r(m)r(n) B(m,n) r(m+n)

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Q: disprove the fallowing A,B and C; of for D PLAUB) - P (A) U P (B) ll

A: Please refer to the image below

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

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Q: 4. Determine whether or not the following are Reflexive, Symmetric and Transitive. (a) on Z: (a, b)…

A: Note:  Since we can do at most three subparts of a question, we have solved the third three…

Q: The order of the element 3 in Z24 is

A: Given: Z24 Formula Used: The order of an element k in Zn is given by Ok=nhcfk,n

Q: Prove the A.B = B.A.

A: To prove AB = BA.

Q: Stefan was able to map AABD onto AABC. D A

A: Given, ∆ABD  and ∆ABC     We have to find whether we can map  ∆ABD  onto ∆ABC

Q: Let f: [a,b]-R be afunction and let c<0, then for any Ac[a,b] sup cf=c inf f

A: We will prove it

Q: 3. cooficiant af z" in the apransion 3)11

A: From the Binomial Expansion

Q: For all intgars a, if 615a, thenbla

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Q: 1. What is the rank of A?

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

Q: Let filN >N be defined by f(n) = Ź v(d) for all nEl din where r(R) is the number of the positive…

A: A multiplicative function on the set of natural numbers is a function T such that Tnm=T(n)T(m)…

Q: 4. Let A C BCR. Prove A° C B°.

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Q: 75. If f(7) = 13 and fis one-to-one, what is f(13)?

A: For a function domain is set of values for which the function is defined. The range of a function is…

Q: Prove that if n divides a, b, and c, then n³ divides a²(b – c) + b² (a – c) +²(b – a).

A: A product is a multiplication of two or more terms and these terms are called the factors of the…

Q: (b) Use the value of det(A) to evaluate 1 2 3 3 -2 3 3 1 1 1 2 -2 -3 -1 4. 1 3 -2 4) 2. 2. 021

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Q: Which of the following things is NOT contained in B? R

A: Given that the plane B, here we have to find the things is not contained in B.

Q: Prove that if r < s < n, then P(n, s) is divisible by P(n.r).

A: Use the formula of permutation

Q: Prove the following. 2. If alc and a+ b = c, then alb.

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Q: 3. Let r and y be positive integers. 4. Let a, b, c e Z. If c divides a +b,

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Q: A(n) __________is a letter used in algebra to represent anynumber from a given set of numbers

A: In algebra, there are different set of numbers such as Real numbers, Complex numbers, Rational…

Q: 49. Prove that (a – b) × (a + b) = 2(a × b).

A: The following properties of vectors are used in proving the given identity. a×a=b×b=0a×b=-(b×a)

Q: If delta is large according to Cohen's classificantion, then the difference between u1 and u0 is…

A: Given that - If delta is large according to Cohen's classificantion, then the difference between u1…

Q: Show that: If |z| = 2, then: z* – z2 – 4| Re < 6 z + 6

A: A complex number z=x+iy are graphically represented as (x,y) on coordinate plane. The polar…

Q: Are the following statements true or false? Justify each conclusion. (c) For all integers a and h,…

A: c For all integers a and b, if a is even and b is odd, then 4 does not divide (a2 + 2b2 ).The…

Q: Prove, using an element-chasing argument, that {15n : n E Z} = {3n : n E Z}N{5n : n E Z}.

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Q: If A is m x n and B is n x m and AB I then the rank of A is

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Q: Let A = A5x 7 be such that rank(A) = 4. Which of the following is equal to the dimension of N(A)? 01…

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Q: founth worlar is

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Q: 3. Show that a2 + b2 + c2 > ab + bc + ca and using this result show that (a) (a + b + c)2 > 3(ab +…

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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: Prove (without expansion) b a c d a -d = (a? + b? + c? + d?)? d -b -c a |-d -c b a

A: We have to prove that abcd−ba−dc−cda−b−d−cba=a2+b2+c2+d22 Consider the left hand side expression…

Q: 7. Establish for A is m × n and B, C are n x p, that A(B+C) = AB + AC

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Q: Give a direct proof of the claim: Vn E N, if the last two digits of n are divisible by 4 then n is…

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Q: 5. Use the in verse motrices to find CAB) (AD ond (2A 22 ー1 4 /- 3. B. 11 2. 3. 3. 2. 2- 2. N/-

A: Given The given inverse matrices are A-1=12114-121123432-2,…

Q: 3. Prove or disprove: If a | (b + c), then either a |b or a | c. h of the follo

A: Since you have asked for question number 3 , we have solved it for you.

Q: Suppose n (a)= 7a + 4, determine a such that n (a) = 39. %3D

A: GIVEN n(a) = 7a+4 and n(a) = 39

Q: i prov

A: Given, -a+b It is proved using axioms of real numbers.

Q: ) Evaluate, using Cauchy formula C:2- (a) zz-l dz dz (6) ( e

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Q: For what values of c is ||c(3, 4, 2)|| 1? (Enter your answers as a comma-separated list.)

A: According to the given information, it is required to find the values for c where:

Q: (а-b) a (b-c)* 3 d

A: a, b, c, d are in continued proportion Therefore, we have ab = bc = cd = k (say) c=dk, b=ck=dk2,…

Q: Let A = {a,b, c} and B = {b, c, a}. Prove that A = B. Thus, the order %3| in which the elements are…

A: The given sets are A={a,b,c} and B={b,c,a}we have to show that A=BResult : two sets A and B are…

Q: Given the set of multiples of 5 defined by 5Z:= {m: m = 5n for all n e Z} together with the…

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Q: Prove that if A,B ∈Mn×n(F) are similar, then det(A) = det(B).

A: If the matrices A and B are similar then there exists a non singular matrix S,

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.

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

A: The relation 'R' = 'is equivalent to' is transitive. Therefore if x R y and y R z then x R z.

Q: (c) If gcd(a , 133) = gcd(b , 133) = 1, show that 133|al8 b18 %3D %3D

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