Determine all values of s so that 1 A = | 1 0 1 1 S is nonsingular.

Q: [ 0 1 1 0 Exercise 8.6.10 Find an SVD for A -

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Q: Solve the Following Euler's (or Cauchy's) Equations: (1) x'y" – 2x² y" – 2.xy'+ y =0

A: As per our guidelines only first question will be solved.

Q: 19. Let a, = (-1)" Vn 2 1. Calculate the value of an+1 - a, for odd values of n. %3D А. -1 В. -2 С.…

A: As this is a multiple question type, according to Bartleby Answer Rule, only 1st question is to be…

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

A: The given matrix will be singular if the determinant of it is 0

Q: x2+1 =0 Has soluion in R

A: Solution:

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 F (s) = then %3D (s+1)2+4

A: Using inverse transform properties, f(t) is given.

Q: Find the nullity of T.T: P3→P1, rank(T) = 2

A: Here given

Q: If AB = B for some B # 0, then A is inertible.

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Q: Let xn ≥ 0 for all n ∈ N. (a) If (xn) → 0, show that (√xn) → 0. (b) If (xn) → x, show that (√xn)…

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Q: Let  A = (1 1 1, 1 2 2) Find R(A), R(AT), and N(A)

A: Given,A=111122the reduced row echelon form of AMake zeros in column 1 except the entry at row 1,…

Q: What is the largest positive constant K such that if 0 O A. e O B. 1 O C. e1 O D. e?

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

A: Given:

Q: Let c be a  positive integer, then (e^c+1)≥e^c for all c.T/F

A: Given that c is positive integer and we have to check whether the given inequality is true or not.…

Q: Let S= (-2, 3]U(4,5). The largest possible value of E SU such that Select one:

A: Given: S = {-2, 3} ∪{4, 5}   To find:  The largest possible value of ε > 0

Q: 2+i3 Evaluate zdz along the following paths- 1+i2 (a) horizontally from 1+i2 to 2 + i2 then…

A: The objective is to slove the above questions.

Q: Let A = 2 2 1 24 2 0 23, 1. Compute L such that A = LU, where U 2. Solve At = 6, where L-¹6 = () 0 =…

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Q: E A B >D Given: AE || FD, EC = BF and ZABF S ZECD. Prove: AB 2 CD. F

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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: Find all values of n such that y = xn satisfies x2y" - 12y = 0

A: To solve the equation x2y''-12y=0, we first need to find y''. y'' can be obtained by differentiating…

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

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Q: Find all values of t for which

A: We are given the determinant of the matrix as 0:   So,           Let's find the determinant of the…

Q: 1 2 1 25 1 1 3 7 2 2 L4 9 3 - 01 Given A = Find the nullity.

A: Given the matrix A=121025113722493−1

Q: Find a and b such that f(x) = ax + ba? +1 has an infection point at (-1,2).

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Q: Assume that |Xn] 0. (Hint: first, prove that P(|X|>c+1) = 0.)

A: Answer:

Q: Suppose A E C such that A(2 + i, 3 – i) = (5 – i,7 – 5i). Then (1) A = (1 – i) (2) A = (2 – i)

A: Given that: 1. λ∈C, λ(2+i, 3-i)=(5-i, 7-5i)   NOTE: As per our answering guidelines, we can only…

Q: Show that g(t) = t2tant takes on the value ½ for some t in [ 0 , π/4 ].

A: gt=t2tant on the interval 0, π4. When t=0, g0=02tan0=0 When t=π4, gπ4=π42tanπ4=π2161=π216=0.6168

Q: Find an explicit formula for s, if so = 1 and %3D Sn =2+2s0 + 2s1 +... +2s, 2+ Sn-1, Vn >1.

A: Generating Functions for a sequence a0, a1,a2,………an,……………… is an infinite series of the form ,…

Q: o.10. Prove that (a) J,"(x) = ¿[J,(x) – 2J,(x) + J, + glw). n n-2 n' n+2

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Q: (a) Let E = {q € Q : V2 < q< 4}. Find sup E, inf E, E, and min E if they max exist.

A: The given problem is to find the Sup E , Inf E , Max E , Min E for the given set E. Given set E ={ q…

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

A: While finding the partial derivative of a multivariable function, if we have to find the partial…

Q: Use Shapiro-Wilks and a = 0.05 for the test and show all parts. * %3D Но: (а) На: (b) F and PValue…

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Q: The linearization at a = 0 to √8+7e is A + Ba. Compute A and B. A B= || ||

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Q: 10. Show that S t2 if 0 1, 2(1 - e-) then Ldf %3D

A: Laplace of differential equation.

Q: Using your software, compute BT B and B BT forDiscuss the nature of the results.

A: Given matrix is  B=11213141516 Transpose of the above matrix is given by, BT=11213141516

Q: 6) In the process of calculating 7s + a In 7s + b L Where a and b are constant, it is obtained that:…

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Q: Find e^z in the for u + iv if z = 11πi/2. (use 3 decimals)

A: Given z=i11π2 We have to find ez in the form u+iv

Q: Find all the joint moments m,1, n and k= 0, 1. . .

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Q: B) If A=0 0 |1 0 01 ,1+0 1 0 prove that A- =(A² + (C + A) + (D + I) 0 0 1 1 C and D are constant 014

A: In this question we have to prove A-1=16A2+C*A+D*I where C and D are constant

Q: Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.

A: By adding the cubes of positive integers we solve the given problem.

Q: Formally prove the T(n) = (5n – 4)° is O(n³). Show all work and all steps to receive full credit.

A: Order: T(n)=(5n-4)3 T(n)=(5n)3-3.(5n)2.4+3.(5n).(4)2-(4)3T(n)=125n3-300n2+240n-64

Q: 4. Prove that (À × B) · (B x T) × (T x A) = [ABT)

A: The objective is to prove that

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

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Q: If t,= 4n+1, find t,, t,, t3, and t Express t n+1, in its simplest form. n+1 In-1

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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: 3 and ajj = i. j. Th

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Q: 27 Find (all) the value(s) of c such that 3cn %3D - 8. n=0 (A) c= 3 (B) c= 4 (C) c = (D) e (E) e (F)…

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Q: 13. a) Show that EX=o (-1)*(")=0, and then verify that ) +C) + C) + - - G) +G) + () +- ... = b)…

A: We will use of binomial theorem to solve it