Find a mat rixP such that P [1 2 1 0 | 1 0 P = O A. -1 1 1 - ОВ. 1 P= OC. 0 1 -1 0 P = O D. 1 1 1 0 OE.

Q: Find a mat rixP such that P-1 I 0 2 1 0 0 2 1 0 P = OA. 1 0 P = O B. 1 1 -1 0 P = OC. 1 1 OD. 1-1 P…

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Q: , Evaluate by interpreting it in terms of areas. *P (2* – I^ + *),J

A: We have to evaluate integral by interpreting in terms of area

Q: Compute det A by first reducing A to triangular form

A: Given matrix is reduced to triangular form as follows.

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

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Q: If sup(S) exists, then it is unique ylgn ihi

A: The solution is given as

Q: GA Given: AC FB TO BC Prove: AB GF

A: Given : GAAC=FBBC To prove : AB¯ ∥GF¯ Proof : If possible let AB is not parallel to GF. So let us…

Q: Given: - L KL ON OP NP Prove: ZM L = 2O * View

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Q: Let m eN and a E Z be such that (a, m) = 1. Let i, j e N. Prove that if om(a) = ij, then om(a') = j.

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Q: Prove that tr(aA + bB) = atr(A) + b tr(B) for any A, B belongs to Mn× n(F).

A: We need to prove that tr(a A + b B) = a tr(A) + b tr(B) for any A, B belongs to Mn×n(F).

Q: Let A € M₂ (R) be given. (a) If AA¹ = 0n, prove that A = On. Does this hold if A € M₂(C)? (b)…

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Q: Let 0 E A CR. Show that if A is both open and closed, then A = R. (Hint: Let M = sup{t: [0,t] C A})…

A: We prove this by contradiction.

Q: Let TE L(V, W), where V and W are finite-dimensional. Prove that rk(7) rk(7*).

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Q: Prove this! P (an) = W/ NM) [M-N (p-q)" ] 8 Npq %3D exp

A: your question is not clear i think some error in the question plz confirm it.....

Q: F. Find Ker() and o(25) for o: Z → Z, such that o(1) = 4. %3D

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Q: 1 0 Find a mat rixP such that P 0 2 1 0 P : %3D 1 0 OB. 1 0 P = -1 1, P = OD. 0 1 1-1 P 3D OE

A: In the question we have to find matrix P.

Q: 30 Find a mat rix P such that P- 1 0 O A.P %3D 1 0 O B. P= 1 0 Oc.P = 1 O D.P = 1 1 O E.P=

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Q: Find a mat rix P such that P 1 0 1 0 P= 23 0 3 1 1 -1 А. 0 1 1 0 P = O B. 1 P = OC. %3D 0 1 1 0 P =…

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Q: m is the mid point of AB find a Of AM

A: Equating the given relation gives the value of x . Then substituting the value of x in the…

Q: .Use the De Moivre's Formula to show that if z = (cose + isine), then z" + ; ÷= 2cos (n8) and (금) 3…

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Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p>1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x<0 when…

Q: K is the midpolnt of GI and HI | GJ. Complete the proof that AHIK E AJGK.

A: Given,            K is the midpoint of GI¯ and HI¯ ∥ GJ¯

Q: Given: ZB ZD Prove:A ABC -A EDC в Ma com A D

A: Explained below...

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: Find a mat rix P such that 0 3 P OA. OB. O 1 P = C. OD. P. OE

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Q: Prove that eie ei(0+2K) ,where k = 0,±1, +2,...., = D

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Q: nd C such that AC=E

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Q: Find a mat rix P such that 30 P%= 1 2 30 0 2 1 0 OAP = %3D 3 -1] 1 0 OB P -3 1 -1 0 OcP = %3D 1 0…

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Q: Let a,b E R with a # 0, b # 0. Prove that (ab)¯1 = a°1b´1. %3D

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Q: ), P{|Zn – c| > ɛ} → 0 as n → o. Show that for any b on g, E[g(Z„)] → g(c) as n→o

A: *Answer:

Q: (a) Let r = ri+ yj + zk and let r = ||r||. Prove that - (1) a

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Q: MN 1 NP, QR 1 RP ΔΟRP Given: Prove: ΔΜΝΡ ~ N R P Exercises 17, 18

A: A triangle with two perpendicular lines

Q: ala lo oepse a ad 1. Let m*(A) = 0. Prove that for every B, m*(BUA) = m"(B).

A: We have to prove the given statement.

Q: Given the bases B = {u,u2} and B'= {u', u'2} for R?, where and u'= The transition mat rix Pg-g' from…

A: Linear transformation problem.....

Q: Prove the following existence proof. P: 3a, y, z E N such that ryz = 24

A: Existence proof

Q: 19. Given: OABCD; BE | MD: M is the midpoint of AB. Prove: DE = BC %3D E D. A M В

A: We have the given figure as, Here, □ABCD is a parallelogram and in figure BE∥MD. M is the mid point…

Q: In ALMN, LN is extended through point N to point 0, mZMNO = (5x – 13)°- mZNLM = (x – 4)°, and m/LMN…

A: Solution-

Q: An Instructor teaching three sections of vering the same material. She has made ction, but she…

A: By using ANOVA test for a single factor, a) Null and alternative hypothesis: Ho:  µ1 = µ2 = µ3  (All…

Q: O let T:R?→R² be a lineas tanafor- mation Such that T([:])- [ ]. T %3D Find matnie A Such that T(x)=…

A: Given that T:ℝ2→ℝ2 such thatT11=41  and T01=32 We have to find the matrix A such that Tx=Ax   ,…

Q: Find the of the GS that satisfies the given Cond hb Sum a n=4 b. h=6

A: Sum of Geometric series.

Q: b. Let x, y,p E Z, where p is prime. Prove that x2 - p²y - p + 0. (Hint: you may use without proof…

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Q: (c) If A E M,(R) is non singular and n 2 2, prove that det(adjA) = (det A)"- (d) If A E M,(R)…

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Q: Let R be a UFD and fx) in REX) So, 0+a € IR.. Show that claf)~ ac(f) a nonzero polynamial

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Q: Question 2: Show that the set S = {rVT + V2:rE Q) is dense in IR. Explain and show your work.

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Q: B. Prove by direct proof general. P: Vn e ZE, (n – 1) (n+ 1) e Z,

A: I have solved B; you just need to expand (n-1)(n+1) and then use the fact that square is always…

Q: Let A EMn (R) be given. If 11x11 = 11yll = 1 and x •y = 1, show that x=y

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Q: Find conditions on a, b, c, and d such that

A: Find conditions on a, b, c, and d such that  B=abcd commutes with both 1000 and 0001 For any matrix…

Q: Consider the following coordinates. W(1,8), X (7,8), Y(4, 5), and Z(1,2) Select all methods you…

A: Given : W(1,8), X(7,8), Y(4,5) and Z(1,2) To find : All methods to prove triangle WYZ  is congruent…

Q: (d) Prove that IJ CINJ. Give an example where 1JÇINJ. (e) Is (ab a e 1,beJ} an ideal in R?

A: ANSWER :

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.