5- The folouing tablo was obtuined from, a polynoinial funetion 1 !2 3 5. ! 14 78 252 620 Determin the order ot poly nomeial and tind the Vaclue of at X = 3. 15 .

Q: 1. 1) Lt c the below figure- be the closed contorer quen in is d Z =-2 i ? so

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Q: (-1)"2" /ñ Prove that if m is a positive interger, 1'(-ni +3) =1:3.5...(2m – 1)

A: I will use method of induction to prove the statment.

Q: vdor (2,1,3) be the {1,)1), (1, 2, >).(O, 1, 0)1 be the {ll,),l), (1, 2,3).CO,1, 0)) linear…

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Q: Howin If Z=RCxy) and u=xayg V=x-y show that 3

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Q: We defined NCE) = ZE for ZE Z Ii]. Prove N (Zw) = NLZ) Ncw) for all Z,W E Z6] .

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Q: 1. Disprove: If A UC=B and AUD=B then C=D. (You may define 2={a,b,c,d,e} for your counterexample.)…

A: As per guidelines we have to solve only one question

Q: 6. Show that the sets S = (1,5) and T = (0, 00) are equinumerous by finding a bijection from S to T.…

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Q: Suppose the conjugate z is equal to the reciprocal 1/ z. What are all possible z's?

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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: Prove that if |z| = 3, then %3D 5 2z – 1 7 - 13 4+ 22

A: The given is related to complex numbers. The solution is explained below.

Q: Use De moivres theorem to determine (3-4))"C4cis 30° )ieave your answer in 10 CiS the Formof Fciso

A: According to the given information it is required to determine the value of

Q: 7. i) Show that Q(2'4,i)/Q is a Galois extension.

A: The given function is, E=ℚ214,ii,e, E=ℚ24,i The minimal polynomial of 24 is  x=24Taking power 4 both…

Q: is a conplex saries of nunbers and for VNEN monert an, bn ER Let 2n- an +ibn. Show that if Ź 2n =…

A: Given:  ∑n=1∞zn is a complex series of numbers and  ∀n∈ℕ, an , bn∈ℝ Let zn= an+i bn To show that :…

Q: 15) o veclovs ú = Givetw and Tñ=211 deternine the projection d on 2.

A: This question can be solved using the projection formula.

Q: (3. Suppose T is a linear tronstormation from V to w and that {š X is a LI. söt of ve ctors in V.…

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Q: (- For all asb,C EZ,prove the folloNing (i)ala,1la, andal0; (ii)0la if and only if a=0; (iit)alb ond…

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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: 1.using the diagrom / mateh the stodenento ad reasans tu whe a two-column that DO =WN. prouf Shaning…

A: Given: DW = ON   To prove: DO = WN   Diagram:

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

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Q: 6. Given: 21 and 22 are complementary Prove: SX 1 WX S. 2,

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Q: 5. Prove that if x, y ER, then x + y ≤ x + y. Use the following cases: (i.) x, y ≥ 0, (ii.) x, y <…

A: We now prove that if x,y ∈ ℝ , then x+ y≤ x+y with the help of given three cases.

Q: c If in is an involution of X, show that (r, y)in = (yi", rin) is an involution of X12). %3D

A: Given X is a lattice. Given in  is an involution of X To show: x,yin=yin,xin is an involution of X2…

Q: Let Xionne Xn be aris H c'cid) From PlO), or QcOi Findthe MP test g sige a to test Ho:G-Be N5 H,:…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: 3. Suppose that BE Mxn(C) and B = 0. Show that I-B is invertible. Hint: Consider I+ B+ B.

A: Given : B is an n×n complex matrix with  B3 = O , where O is zero matrix. To prove :  I-B is…

Q: @ Let A -a Find Cenditiens on a,b.c and d that AX =o has infailely many Solution. what must there…

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Q: 1. Decide if the following statement is True or False: %3D Let A1, A2, ..., Ak E Mnxn(R) be such…

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Q: 10. Let C : N × N → N by, for all (x, y) EN x N, (x + y)² – 3z – y+2 C(t, y) = (i 1) +y = Ei 1) + y-…

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Q: Let gilx) i for n z2 i define gncr) -gn1(g,(), = 2ー× Deter mine the Intervai Such that g2avu CA) is…

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Q: Showw Fom yex)=D90Y,(x) + a, y,(x) that seris sol utron is of the hene y,cx) contains only even…

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Q: _. . Prove that z² = + Emo(-1)" (n + 1) (²2)", where |z-21 < 2.

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Q: c If in is an involution of X, show that (x, y)in = (yin, xin) is an involution of X2). %3D

A: Let X be a lattice We have to show that (x, y)in=(yin, xin) is an X[2] X[2] is a 2 x 2 matrix We…

Q: (2 Let xinN(0.1), n = 2 and T= Xx +X2 Show that Tis a Sufficiency Stakistic.

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Q: Fiven with z1 = (-3,1) and z2 = (1, 4). Show that |21 2| = |21||2|- %3D

A: Complex number and it's modulus

Q: Prove that Z(D,) # {1} if and only if 2|n (hint: if 2|n look at ri).

A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…

Q: Prove that A N (BU C) = (A N B) U (A N C) by giving a Venn diagram proof. Label your diagram(s)…

A: Venn diagram are pictorial representations of mathematical or logical sets of data as closed curves…

Q: enoitetimil torte stigasb = 4", where m, neN. 10. Prove the identity: 3 r=0 itong s

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Q: 9. Glven ABCD wth A(2,3), D(4,0), C(8,9), D(6, 4). N Ihe dlagonals Intersect at point E, what are…

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Q: Let C: |2 | 4 and I 6 de Then O None of these OF0 (WithoUi applying cauchy Goursat Theorem) O Ho by…

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Q: 4) Let (an) be anumsenical seguence sveh that lin u"4, Then the nadius of Comvergonce of the beries…

A: The given series is: ∑n=0∞7an2xn. We will use the root test to find the radius of convergence.

Q: ) Prove that Вiт.m) - I(z)(m) for m >0 22'T(m +) 2

A: We use the property of Beta function and relation between Beta and Gamma function to prove the…

Q: 1 Brandt r at an ans monthly within a • Deter order b Find

A: Introduction: The formula for a monthly payment of loan amount is given by, A=Pr1+rn1+rn-1 Where P…

Q: 2くメくwhich of thhe Polowing Statements about X are nec. sS ar:ly true sand which are not 1ecessarilly…

A: Given that 2&lt;x&lt;6.......(1) We have to show which of the following statements about x is…

Q: and lo le elemento fa boolean Algehna 6 Yt a Lot a06 = ab + a'b' (kquivelence"). Prove that laob)oc…

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

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Q: the set of real numbers R there is de fined as: 21 xy = 23 +y3 that (TR, x)is Abelian G Proye

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Q: 5) Let Re(z) and Im(z) denote respectively t parts of z, show that:- 2)z+z= 2Re b) Z-Z= 2i Imn( z)…

A: Given

Q: 3.1 For Aand B subsets of the univers al se tx iprovide a formal prost for: A x CBu C) is a subset…

A: Let A, B  and C are the subsets of the Universal set.   We have to show : A×(B ∪ C)  is a subset of…

Q: 5. Let A z 3 4 87 8- ーん Prore that find ite diogonel form. A it diaganalianllen and

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

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.