Given: e || m Z3 = 24 1 Prove: e || n m 3 4

Q: 4. Let F = {s+t√2 s,te Q}. Show that F is a subfield of R. You may assume that √2&Q.

A: The objective of the question is to prove that the set F, defined as F = {s + t * sqrt(2) | s, t…

Q: Corollary 6.9. Let X; ~ N(m;, o?), i = 1,2, where X1 and X2 are indepen- dent, and let Y = X1 + X2.…

A:

Q: Let D = {1, 2, 4} %3D Let P(x) be the predicate "x - 2x 0". Is it true that Vx E D, x- 2x > 0?

A: Proving by counter example.

Q: Show that A = (aj) = Cmxn. Then || A||2 ≤ || A||F ≤ √ Rank(A)|| A||2 V

A: Matrix A=(aij)∈Cm×n: This notation indicates that A is a matrix with complex entries, where m and n…

Q: S S-a₁ + S S-a₂ ++ n² ≥ S-an n-1' S ZZUA

A:

Q: 1. S ef = c f

A:

Q: 까지 dx 10. A. In x + C B. In² [x] + C C. m² 1x1 xl 2 + + C

A:

Q: 8.k Let F C RP. try the following items a) F is closed in RP if and only if F = F

A:

Q: Q3: If P(X= x) = a 8(x) + b 8(x + 1); then a + b = A) 0.5 B) 0.3 C) 0.4 D) 1 E) None

A: Given: P(X=x)=aδ(x)+bδ(x+1)

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: Let M = {x + 1, x2-2,3x). %3D Which of the following statements is true about M? O None of the…

A:

Q: 1.2 Determine if the following statement is true or false. Motivate your answer. If Re(z) > Re(w)…

A:

Q: 10.3.7. As usual let D8 g² = e, gf H = = = (a,b | a4 = b² = e, ba f2g). Let G {e} x D8 ≤ G. (a) What…

A: image uploadedExplanation:Step 1: Step 2:Step 3: Step 4:

Q: 1 d. p(0) [Note that p(0) : к (0)

A: It is given that rt=sint, t, cost. Recall the formula for the curvature, κt=r't×r''tr't3. Obtain the…

Q: (a) Consider the following true fact: For all n, m € Z \ {0}, if ged(n, m) Is the converse also…

A: If Converse of any one of the above is not true,  then we will discuss it with the help of…

Q: Prove that : L²₁ (1-x²) Pm Phd x T 0. 2n (n + 1) 2n + 1 4 mn. m = 11. m, ne N

A:

Q: dt 20.5 t2+2t A - In|t? + 2t| + C B. 2ln +C C. In +C D. In + C

A: First we common out t2 from denominator and then put 1+2/t=u and differentiate both sides with…

Q: If fo) = x + 1 then (/(2r)) at x= 1 O a. 2 O b. 1 Oc8 O d. 4

A: This question is about differentiation of functions

Q: Let Z - N(0, 1). Find P(Z < 2). Question Help: D Post to forum

A: Given that, Z~N(0,1)

Q: r r 2r p 2r 3r p 2r 3r 4r .. .. .. m 2m 3r nr Show that S 1 and 0 < r < 1. [Hint: E, iri < (1-r)²…

A:

Q: Given d, = and dy = Then d, and d, are not - conjugateif Non of these O D

A: Given d0 = -11  and  d1 = 56

Q: 3.3. Let a, BEC. Prove that la + B2 + la – B|2 2(la|? + |B|?), and deduce that |a + Va? – B2|+ |la –…

A:

Q: Let A = 0 00 G|5 0 0 0 , u = 1|5 15 10 - 25 and v= g d h Define T: R³ R³ by T(x) = Ax. Find T(u) and…

A: Let and ,Define Then,   and

Q: Let f(x, y) = x(y - 3) and F = Vf. If r = with 0 ≤ t ≤ 2, then [F. dr is equal to: a. -7 b. -11 c.…

A: We find the line integral in the following way

Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

A:

Q: Prove that re" = 3 – x² for some negative value of x. [Hint: Use the IVT]

A: According to the given information it is required to prove that: xex=3−x2 for some negative value of…

Q: IS T-dist prove o E(T)=0 QvarしT)=て %3D V-2

A:

Q: GIVEN: k || l, 5 = x8. PROVE: j || l. 56 3 4 1 2

A:

Q: Problem Statement Assuming x e Z. Prove 2|(x – 6x + 5) = 2+ x alb keZ a 3|6 is True because = 2 €Z…

A:

Q: A. Evaluate the follow 1. S dy 3+√y+3

A:

Q: Let q E Q and x E R - Q. Prove that q + XER - Q.

A:

Q: 95. Prove that ||v - w2 = ||v|2 + ||w|2 – 2v • w. 97. Prove that ||v + w|[² + |v – w|? = 2(||v||² +…

A: Note:- We’ll answer the 95th question since we answer only one question at a time. Please submit a…

Q: 2 4 Q2) Assume A = |1 3 and B = show that (AB)' = B' A' 3 4] l3 6 4

A:

Q: 9. Prove or disprove. (a) Vn e Z*, n² < 2". (b) Vm e Z, if m is odd, then m² is odd.

A: In this question we have prove if this equation are valid or not.