(c) Let z1 = 2+ 2i and let 22 =1+i. Prove that the triangle inequality |21 + z2| < |21| + |22| holds.

Q: . Rewrite the equality of ideals (r+ y/2) = (3 – 4/2) in Z[/2] in terms of elements.

A: We know that, A subring  B of a ring R is called a ideal of R if for every r∈R and for every b∈B,…

Q: ind the three positive numbers I, y, and z with minimal sum whose product is 64.

A:

Q: Find real numbers x and y such that iy 2 - i i + 3 1 + i ||

A:

Q: ||x||3 < ||x||1|||| VI 22

A: As it is known, L2 norm of x is given by x2=∑i=1nxi21/2 L1 norm of x is given by x1=∑i=1nxi L∞ norm…

Q: Express K#S^2#T#2P as a connected sum of projective planes or as a connected sum of tori.

A: To express the given connected sum (of surfaces) in the required form

Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

Q: Solve the Ssy stem by graphing. S2x+3y=6 he+ hei-ニsっ What is te soloution set?

A: We have to find the solution set of the given equations when they represents a graph. A solution set…

Q: To prove the Cauchy-Schwarz Inequality u v < ||u|| ||v||, for any real number t, 0 < (tu + v) · (tu…

A: Let u and v be two vectors and a, b are real numbers. Use the following formulae, to prove the…

Q: a b (6) Identify all of the nonempty submatrices of A = с d

A: Given that:Matrix A = abcd

Q: Q[V5]is Principal Ideal Domain. True False O O

A: If Q5 is a field, then it will be principle ideal domain. It suffices to show that every element of…

Q: ?, R(A)IN(A*)

A:

Q: Solve the following inequality graphically in two-dimensional plane:2x – 3y &gt; 6

A:

Q: 2] a) If Á. B = AB cos(0), then show that |A. B| < |A]. |B|.(Cauch-Schwarz inequality).

A: I am solving question 1 if you want second question then repost.

Q: B = and C: .Prove that A = B² =C? = 1. 3. Given A = %3D

A: Given: A=0110, B=0-ii0, C=100-1 We know that for a 2×2 matrixP=abcd, P2 is given by…

Q: Question 5 Use the Cauchy-Schwarz inequality to show that if a1, a2, . .. , an are positive real…

A:

Q: b- Let X₁, X2,.... Xn b (a) Find a complete (b) Find the UMVU

A: Solution:   (a):

Q: seS/ast?dep=280917 Verify the Cauchy-Schwarz Inequality and the triangle inequality for the given v…

A:

Q: 5. (a) Describe and sketch the set of points in the complex plane satisfying the inequality: 1< |z…

A: The set of points shown will be bounded by two circles centered at -1,3 of radii 1 and 3.

Q: Solve the folowing equation on [0,2pi) 2sqrt2 +4cosx=0

A: In the given equation, the cosine function is the trigonometric function:   Rewrite the given…

Q: Use the I.V.T and Rolle's Theorem/M.V.T to prove that the equation below has a unique solution in…

A:

Q: 8. Work out a Gaussian quadrature formula of the form Ans. A; = 1, x; = Aif(x1) + Arf (x2). f(x) dr

A: The given problem is to prove the following integral, the proof is to show the 2 point gaussian…

Q: 4. Prove the Triangle Inequality: If v, weV, then || v + w ||<|| v || + | w || -

A:

Q: Q[V2]is Principal Ideal Domain. O True False

A: We have to solve given problem:

Q: 2. Prove this using indirect proof in two-column form. Given: MP 1 NO M Prove: ZNPM is not a…

A:

Q: 3. Find the constants bo, co, a1, b1, C₁ so that So(x)=1+ box + cox² + x³, S(x) = { S₁(x) = a₁ - 2x…

A:

Q: 2. Find the (infinity norm) condition number of 2.01 1 (b) A = 3 6.

A:

Q: %3D n-0o 2n

A: Given. We are given a limit and we need to prove that the limit of the given function at infinity…

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

A:

Q: 3. Prove that R² is Hausdorff. Is R²T3? Is R² T4?

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 3) Prove the following statement using the Intermediate Value Theorem (IVT): 2ª + 3* = 4* has a…

A:

Q: If u, v are given unequal numbers anu (un-1+ Pn-1), vn = V (u –1 Vn-1), where n2 2 , %3D Un %3D 2…

A: Given

Q: 2.2.7. Prove the full triangle inequality: for every x, y E R", | |æ| – |y|| < |x± y| < |æ| + \y]-…

A:

Q: - Use the Exterior Angle Inequality to find an upper and lower bound for LMLK = y. %3D M 70° 50 K L.

A: Given: To Find: The upper and lower bound for ∠MLK=y° using exterior angle inequality

Q: • Verify that 3r is a one-parameter family of solutions of the DE ry + y = 3r. • Deduce a solution…

A:

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

A:

Q: Prove that Ix I - I y I &lt; Ix - y 1-Hint: Apply the triangle inequality to y and x - y.

A:

Q: R.2. Prove that if A and B – C are disjoint, then AN BCC.

A:

Q: Solve the following inequality graphically in two-dimensional plane:3x + 4y ≤ 12

A: We first graph 3x+4y=12 line We make a table for it x 4 0 y 0 3

Q: Solve the following inequality graphically in two-dimensional plane:– 3x + 2y ≥ – 6

A: We first sketch – 3x + 2y = – 6 line We will use a table for this x 0 2 y -3 0

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: e[V5]is Principal Ideal Domain. True False

A:

Q: Using Euler’s formula but not using Kuratowski’s Theorem, prove that K5 and K3;3 are not planar.

A: We need to prove K5 and K3,3 are non planar graphs. For that we must use Euler's formula. The…

Q: B. Prove the Triangle Inequality Theorem using Indirect Method. Given: AABC. Prove: AC + AB > BC

A:

Q: 2] a) If A. B = AB cos(0), then show that |A. B| < |A|. |B|.(Cauch-Schwarz inequality).

A:

Q: Let F1 and F2 be 4-dimensional flats in R6, and suppose that F, N F, # Ø. What are the possible…

A:

Q: ■ Show that the area of the triangle whose vertices are the [X1 У1 points (x₁, y₁), (X2, Y2) &(X3,…

A:

Q: 4. Prove the statement of 3 on page 9 of lecture notes 10, i.e., SSE xa-1)(0–1)*

A: The given model is, yij=µ+Ai+Bj+∈ij    where, i= 1, 2.......a and  j= 1, 2.....b∈ij~N(0, σ2∈)Testing…

Q: Determine the ratio and interval of con (-1)"x" in=0 n6" O R.O.C=6, 1.0.C: x E [-6, 6) R.O.C=1,…

A: Here we have ∑n=0∞(-1)nxnn6n=∑n=0∞an ⇒an=(-1)nxnn6n