1. Show that for all z1, Z2 E C, Then we have: |Z1 + Z2| < |Z1| + |Z2|

Q: if A) B) none of these a(n) a(n) is smaller or equal to oo then is finite

A: In the question we have to select correct option.

Q: 19 + 4x. Determine the zero(s) of q(x) = x

A: Recall: zero(s) of q(x) is set of all values of x in which q(x)=0 Given: q(x)=-19+4x

Q: Let x, y E R. Prove that if 21x + 35y = 45, then x and y are not both integers.

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Q: Prove that if both y and z are solutions to x' = Ax, then for any c1, c2, the function c1y + c2z is…

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Q: If z1 and zą both satisfy z +z = 2 |z - 1| and arg (21– 2): then find Im (21 + z2). 4'

A: let z1 = x1+iy , z2 = x2+iy2

Q: Show that if ax2 + bx + c = 0 for all x, then a = b = c =0

A: It is given that, ax2+bx+c=0 for all x,  To prove a = b = c = 0

Q: x is even and v is any integer, then their produc

A: If x is even then x=2m where m is any integer y is any integer,  Case I Let y be even y=2n where n…

Q: 2. Suppose f: A → B and Y and Z are subsets of B. -1 (a) Will it always be true that f'(Yn Z) = f'…

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Q: 3.19 Suppose if r = 0, f(x) = {-1)" if r E n+1' n where n E N. Prove: f € R[0, 1], even though f has…

A: Sol

Q: Prove that ifx > 3 and y> 4, then xy > 11.

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Q: Let X and Y be defined as follows: X = {a E Z | a = 3x for some x E Z}, and Y = {b E Z |b = 3y – 3…

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Q: 2. Find three positive integers x, y, and z if their product is 27 and the sum is a minimum.

A: Given three positive numbers are  x, y, and z Product = xyz = 27 And sum is minimum

Q: Show that for all z1, Z2 E C, Then we have: |Iz1| – |z2|| < |z1 +z2l

A: 2) The inequality can be proved as follows:

Q: Suppose: n ≥ 3 and x,y ∈ Rn , |x - y| = d > 0 and r is some +R, Need to show: 2r = d, there is…

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Q: 5.1. Show that y2 , V2 , and v3 + V2 algebraic. are

A: We will use definition of algebraic numbers

Q: 11. Solve the following and state the restriction(s) on x : x- 2 a) -3 2x+3 3 >2 2x+4 b) X+3 X+7 c)…

A: To solve the given equations and find restrictions on x

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

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Q: Determine x[2] and x[3] given (a) 2x[n+2] – 5x[n+ 1] = 4n, x[1] = 2 (b) 6x[n] – x[n – 1]+ 2x[n – 2]…

A: Given:  a) b) c)

Q: 11.32 question attached. Thank you for answering my question!

A: It is given that X and Y are independent normal random variables.The required probability is:

Q: Suppose we observe X1, X2, ..., X U (0, 1). Show that nX(1) 4 Exp(1). с.

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Q: The characteristic of Z3[x] is 6. a) True b) False

A: Determine whether the given statement is true or false.

Q: Determine if the following is a fundemental set of solutions to  y'' -6y' + 25 = 0 Given that…

A: If the Wronskian of two solutions is not equal to zero, then the given set of solution is…

Q: GIVEN: 2x - 3 = 7 PROVE: x = 5

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Q: (1) Use the definition to prove that if xn → 2 then (2xn + 1) / xn → 5/2.

A: As per our company guideline we are supposed to answer only first three  qs, kindly post remaining…

Q: Let S be the set of integer solutions to the equation x1 +x2+x3+x4 = 30, where x; > 0 for i = 1,2,…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 1. Let A = {x E Z | 6 divides x} and B = {x € Z | 3 divides x}. Prove that A C B, and then prove…

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Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + z2| < ]z1]+ |z2| 2. Show that for all z1, Z2 E…

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Q: If A is a 2 x 2 with det(A) = 3, then det(4A1) = %3D

A: det(A-1)=1det(A) det(4A-1)=4ndet(A-1) where n is the order of the matrix.

Q: Show that for any positive integers i and j with i > j, we have T;(x)T;(x) = [Ti+;(x) +T;-j(x)].

A: we have to show, for any positive integers i and j with i&gt;j TixTjx=12Ti+jx+Ti-jx Now, we know…

Q: Supposernc N and n 4 0 Then show that rn is positive if and only if r is positive

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Q: show that if Z ~ N(0, 1) and Y ~x²(n) with Z and Y to be independent, then T: n

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Q: Let P= {p:p=6x-1, for some x EZ} and Q= {q:q=6y+5, for some y €Z}. Prove that P= Q

A: Answer

Q: Suppose A · B = 0. Show that this implies that C(B) is contained in Null(A).

A: Suppose A.B = 0 then we have to show that  Column space of B contained in the null space of A  i.e…

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: If X is uniform on [-2,2] then p(x <0) = 1 1 2

A: X is uniform on [-2,2]   a = -2,   b= 2

Q: Suppose X~ N(u=120, o = 3), determine the value of x such that P(X>x) = 0.05.

A: Given that X follows N(mean = 120, SD = 3), then Z = (X - mean)/SD follows N(0,1)

Q: Show that r(r+3) Hence, Show that 1 +. 2.5 1 1-4 3-6 n(n+3) n+3 n+2 n+1

A: Using series

Q: Which of the following is a fundamental set of solution of y" – 2y' + 5y = 0.

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Q: If var(0) →0 as n→ ∞, then 0 is said to be Select one: a. efficient b. unbiased C. consistent d.…

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Q: True or False? If d = gcd(a,b), then there exists integers x, y such that d = ax +by

A: solution.

Q: Show that if (B) (C) = 3x N (AB)_ (BC) (CA) =y, N (A) = x, = 2x, and N N N then the value of neither…

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Q: If the statement is true, prove. If the statement is false, disprove. 1 + 2" > 3n for all n E Z

A: False.  take n =2

Q: x | X> 3) =? and E [X | X> 3] =?

A: X ∼ exp (λ)  having pdf  f(x)=λe-λx      x&lt;0

Q: (28) Suppose 1 <N < w and h : w → N. Show that there exist a < b < c < d <e<w such that h(a) = h(b)…

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Q: 4. Find the dual of the following LP: max z = - 4x1 - X2 4x + 3x2 6 X1 + 2x2 s 3 3x1 + x2 = 3 s.t.…

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Q: Prove the following:  if x^2 = y^2, then x = y or x = -y.

A: Subtract y^2 from both sides.

Q: Which of the following conditions is sufficient to guarantee that integers x, y, and z satisfy the…

A: x(x-y)+y(y-z)+z(z-x)=1 Put all the given conditions and check which one is valid.

Q: Let x, y e Z. Prove that if 3x + 7y is odd or 5x + 6y is even, then x or y is even.

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Q: Let P= (p:p=6x-1, for some x EZ) and Q = {q:q=6y+5, for some y EZ}. Prove that P=Q

A: