1 -4 Let A = a E SL2(R). Find a first then find A 9.

Q: Ex 3.5.1 Let a = 3 .5-7. 13 and b = 2 -* .5.7.11 - 13*. Show that a|b by finding an z such that b =…

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Q: Property 9. If u, exists, then µ' exists for all '13 s <r. Mathematically, if E (X") exists, then E…

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Q: 4.) Find the value(s) of k such that A is singular. 1 k 2 A = -2 -k 3 1 -4

A: The given matrix is                               A=  1  k    2-2  0 -k   3  1 -4 We have to find…

Q: 12. E1 Find the sum of the following sigma notations. Given: X=2 X4 = -2 X2= 3 X5=1 X6 =-3 13. E1*1…

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Q: A. let w-e te Find W2

A: We can solve this using u/v rule

Q: 1. Prove That E (ri + si) a; = E}-1ri a; + £?=1 Sį a¿ 2. Find E(-1)k+1 (2k) k=1 3. Given X = 2, 4,…

A: 1)  LHS=∑i=1n ri+si ai          = r1+s1 a1+ r2+s2 a2 + ..................+ rn+sn an          =…

Q: Let n e N, s > 0, a > 1. Show that n! 1"e" dr sn+1 Inz dr 1 (a – 1)2

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Q: If z + In(e 2 – e" + e*) = 0 -2x az find at the point (0, 0) O-3 O 3 O-2 O 2

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Q: Example 8.13. Use Simpson's 1/3rd rule to find dx by taking seven ordinates.

A: Here we have y=f(x)=e-x2 now to take seven ordinate means n=6  (6 intervals) then step size…

Q: Example 7.13. Apply Bessel's formula to obtain y25 given y20 2854, y24 = 3162, y 28 = 3544, y 32 =…

A: Here we need to use bessel's formula to solve this problem.

Q: つ1 BC. T (o,f)= 1 , T(h,f) = (os f. エ、(.T(メ,o)= ズ.

A: According to the given information, it is required to solve the heat equation.

Q: 3 4 Let A be 4 -3 la. Set up the characteristic equation and own value for A

A: :GivenAs per our guideliness we are supposed to solve only one part. Please resubmit other part…

Q: Find a given that ||a i+ (a – 1)j + (a + 1)k|| = 7.

A: Given:

Q: Let X₁, X2, ..., Xn be a r. s. of size n from N(0₁,0₁). find the m. l. e 0₁ and the corresponding M.…

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Q: 24- 'ח 27 Given : x³sin(2x)dx = Find b if sbsn 64

A: ∫0bx3sin(2x)dx=27π2-2464 First finding the indefinite integral ∫x3sin(2x)dx(integration by parts…

Q: Let w = x. In(xy² z® ), then which of the following is a. O b. 0 -2 d. 22 O e. C.

A: G

Q: 2.. This question should be done by hand. Let 3 0. A = b = 0 -1 Use the spectral method to obtain…

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Q: 3 6 6 0 4 Let C = and D= |2 -6 7 -4 -1 Find DC if it is defined. Otherwise, click on "Undefined". DC…

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Q: Sa 1-rh+1 Prove that E-0 ar! F,r # 1 1-r ((n + 1)a,r = 1

A: For r not equal to 1,   The above given summation is geometric progression of first term=a and…

Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

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Q: 1)z = e(4+j3) In(6230") 2) z = (-;)(* 2) z = (-)(r)"

A: (1) The  given complex equation is                                                Z=e4+j3ln6∠30°

Q: -ST In 0.2 %D 1-8

A: To solve the equation for δ, first we remove square root by squaring both sides and then get an…

Q: Let a be a constant. Given that 3x In(ax)dr = e18 ( 36 -89 , find In a. 3

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Q: Question- let G De 4. H and k. then of ZLHS and 2

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Q: 84. a. Prove that e > 1 + x if x > 0. b. Use the result in part (a) to show that e 21+x + r.

A: Answer (a): To prove : ex≥1+x if x≥0 The given inequality can also be written as: ex≥1+xex-1-x≥0

Q: QUESTION 5 Let a ={An :n €Z), where A =[-n, n]for each , E7. Then, NA nEZ %3D For the toolbar, press…

A: We have to find the infinite intersection of given set.

Q: If y = E£o (k + 1) æk+3 then y' = Eio

A: A series representation of a function y(x) can be differentiated term-by-term to obtain a series…

Q: 98 unfornly distributed the death cre CHX+h) then nen 2n+n M Prove t 2+h pmx

A: If the deaths re uniformly distributed in the interval (x,x+n) Then  qnn=2n*Mxn2+n*Mxn suppose qnn…

Q: (+7.,(9-3) p ind G LD (+) t S+1+ひ!S

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Q: 2) Suppose A E M„(Z) is. Show: A) If det(A) = +1 then A-1 e M„(Z). B) If n = 2 and A-1 e M,(Z) then…

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Q: 10) Let A E Mnxn be given by 0 0 ao ... -1 .. A = -1 0 a2 .. 0 0 0 • -1 an-1 .. Compute XA(t).

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Q: 2 1.5 0.6 09 1.2 Reason for similarity?i * SSS- * SAS- H AA 1 NNS

A: SSS (Side-Side-Side) SSS Similarity Theorem: If all three pairs of corresponding sides of two…

Q: 2. 1 3 Let A = |0 2 -1 Lo 2. a) Show that (A – 21)³ = 0 . Calculate e4-21 b) Use the fact that A(21)…

A: (a) We have…

Q: QUESTION 10: (4 Prove that V n E N, 1+3+ 5 + -.+ (2n – 1) = n².

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Q: 17. Let a, = (-1)" vn 2 1. Calculate the value of an+1 - a, for odd values of n. A.-1 В. -2 С. 2 D.…

A: Given sequence is  an=(-1)^n

Q: Find L{{t"+3)*} O none of the choices given n! sn+1 n! 2. +6 S2n+1 n! 6. sh+1 (2n)! n! s2n+1 +6 sn+1…

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Q: -2) Calculate A-1 by 2 Let A = 1 2 1 -1 -1 A-' = ÷(-A² + 3A +I). and verify your result by showing…

A: Given: A=12-2121-1-10 Therefore,…

Q: 3 (5) Suppose that T : R³ → R² „such that 2 1 1 T (e,) = T(e.) T(e,) = and T (e,) = 1 1 3 2 T Find -…

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Q: Find the value(s) of k such that A is singular.

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Q: 8. Let 2ni S7 = e7 = cos- 27 + isin- 7 7 a. Prove that E¢ = 0 k=0

A: we have ζ7=e2πi7=cos2π7+isin2π7we have to prove…

Q: -1 0 0 Let 0 1 Calculate A20 + I3y3 + A. 0 0 -1 Select one:

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Q: et A E C. Show that |A| 1 if and only if A= e for some 0 E R. %3D

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Q: 1. a) In G = (Z43, e), find [G:H] for H = (32). b) In G = (Z54, O), find [G: H] for H = (24).

A: 1. a) Consider the group G=ℤ48, ⊕. We know that the set ℤn=0, 1, 2, …, n-1 forms a group under…

Q: Let z~N(0,1). Find a constant c for which P(-c <z< c) = 0.8664

A: From the provided information, X~N (0, 1) P (-c &lt; Z &lt; c) = 0.8664

Q: If we know that E (") (x" 1) = ("†").t then show that Eo (") -C") r3D0

A: Given information: The given theorem is:

Q: Theorem 17-2. Let {T„} be a sequence of estimators such that for all 0 e 0, and (ii) Vare (Tµ) →0,…

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Q: 3. Let X Geometric(p) with p e (0, 1). Prove that for every a, beN we have P(X = a + 6|X > a) = P(X…

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

Q: 3. Given 1 1 -j -1 j A = 2 1 -1 -1 -1 -j] where j= -I. (a) Calculate |||1, || 4||2, and ||||p. (b)…

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Q: 5. Let M = [-24 3]. Determine a constant C such that (CM)( CM") = [261]. Is there more than one…

A: Given M=-2 4 3