how that ℝ3 = span( 1 1 2 1 2 1 0 3 -1

Q: %3D 2. Prove that -24y of 3. =2x

A:

Q: Prove that Σ (2n+1) P(x) no (1-2hx+h²) ¾/2₂

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Q: Let x, y ∈ R. Suppose x^2 +y^2 = 0. Prove that x = 0 and y = 0.

A:

Q: If W(-10, 4), X(-3, -1), and Y(-5, 11) dassify AWXY by its sides. Show all work to justify your…

A: Given,           If W-10, 4, X-3, -1, and Y-5, 11 of ∆WXY.

Q: Find all numbers z such that Az3 + Bz² + Cz = D %3D B = [2 4 21 1 1 1. A = 1 3 1. 1 -2 2 4 21 C li 3…

A:

Q: Suppose the conjugate z is equal to the reciprocal 1/ z. What are all possible z's?

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Q: 4. Prove that (À x B) - (B x C) x (C x A) = [AB %3D

A: The solution is given below.

Q: Y Show that f (2)= 2+ Con formal maps %3D on %3D

A: Given that,f(z)=z+1zz=1

Q: "he pmf of X is 4.x – 1 - fx(x) = where x = 1, 2, 3 %3D %3D to

A:

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: Prove that the quartic function q(z) = r* - 16 has only

A: Given that: q(x)=x4-16

Q: a+ib a) If x+ iy = prove that x? + y² = 1. a-ib

A:

Q: 2) Let R' real numbers, define = x,Y1 + 3x2y; + 5x3y3 for x = (x, X2, X3) and y (y,Yz, Y3). Is…

A: Given x=x1,x2,x3, y=y1,y2,y3 in ℝ3. Define x,y=x1y1+3x2y2+5x3y3

Q: 5. What is UF, where F = Ø? Prove the correctness of your %3D | computation. answer

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Q: 1-a*** a zi i. La 1-a

A:

Q: 5. What is UF, where F = 0? Prove the correctness of your %3D answer / computation.

A: To find- What is ∪F, where F = ∅? Prove the correctness of your answer/computation.

Q: - Show that the area of the triangle whose vertices are the [x1 yi det X2 Y2 A - points (x₁, y₁),…

A:

Q: Let X,X2, ,X, be a ranc *(X), = 0*(1– 0)1-x; %3D

A: from above distribution is binomial  f(x)θ=θx(1-θ)1-x  ;0<x<1 E(x)= nθvar(x)=nθ(1-θ)…

Q: Prove that Lim + Tene + …+: 1 %3D ... 2n²+1 V2n²+2 2n²+n.

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Q: let (X, Z) %3. üit piece wise comnected ?

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Q: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at

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Q: Let r, y EN such that y # 0, then y+r#0.

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Q: Verify that (AB)" = BT AT %3D التحق ق 3 2 4 2 1 3 A = 2 1 B =1 2 5 4 2 3 0 2 1

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Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

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Q: 2. Use the Squeeze Theorem to show that f(r) = 2 is in R(0, 3).

A:

Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: Find all valus of z such that (5 + z)6 = (1+ i)z6

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Q: Show that f: R → R defined as f(a) = 3a³- 4 is a one to one %3D iuicuon.

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Q: , Y, 2, W) w) 3. Using methods of linear algebra verify whether Question a. span{(2,0,0), (1, 3,0)}C…

A:

Q: Find (T3 • T, o T1)-1 if Ti 1(х, у, 2) %3D (х - у, — у, х+2) T."(х, у, 2) %3D (х -у+z, 0, 3x) T(х,…

A: This question is related to linear transformation . See 2nd step.

Q: Show that  ℝ2 = span([1 1], [1 -1])

A:

Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

Q: 3. 2. If A is 2x2 matri x aud Á = A, but %3D A+ A. show that A= 0

A: The solution is :

Q: LZHP - DTNV. Complete the statement below. ZZ = _2_

A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

Q: Calculate A and B so that t B %3D 1+1 (1-z²)

A:

Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: Find all triples of integers (x, y, z) that satisfy x² + 2y² = z2.

A:

Q: Use Cramer's rule to solve for z. Зх — 4у + z %3D 3 2х + 3у = 8 5y + 8z = 11

A:

Q: Tofology 2. EX しT X={12/3/4 /5,6 T=Eメ,中っをり,立る, りろ4。 LeT {1,3,4), Topology ? زژه اوم.

A: For the given statement

Q: Show that ag = vp¤(ax+1 + 1) %3D

A: Given  ax=vpxax+1+1

Q: Find the cemplex fourth routs of Z: 2 J3-22

A: Given, z= 2√3-2i Therefore, r= √[(2√3)²+(2)²] r= √(12+4) r= 4 θ= tan-1(-2/2√3) θ= -30°

Q: prove using soundness that the converse of Axiom 2: (vx)A → A[x := t] is not a theorem

A: Solution: If Î" ` Ï• then Î" |= Ï•. Completeness If Î" |= Ï• then Î" ` Ï•. Thus, any formula proved…

Q: Use Green Theorem to Evaluate y x²dx – x²dy where C is left half of x² + y² = 25

A: Note that left half of the circle x2+y2=25 means the second and third quadrants. Now, in the second…

Q: What theorem shows that GTY = GUX? Osss O SAS O AAS O ASA

A: We have to check

Q: Let S = {2x, 1 – x, x² + x – 1,x + 1,x – 2}. Then %3D P3 P2

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Q: Prove that Srxdr = 2[, , da, r × dr =

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Q: Let z = 2 - 3xy?+ x². Zay %3D Zyy

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Q: Prove: |I| = 1. %3D

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Q: If Ø : R3 → R3 be defined as Ø (x,y,z) = (2x, 4x –y,2x+ 3yz) then show that Ø is invertible. %3D

A: Given that ϕ:R3→R3 is defined as ϕx,y,z=2x,4x-y,2x+3yz. Now, ϕ is invertible if ϕ is one-one and…