Show the statement below using Zorn's lemma. Let a1, a2, ·.. , an be uniquely different elements of A CR and r1, r2, .· , rn a rational number, then ria1 + r2a2 +…… ri = r2 = .: = rn = 0 +rnan = 0= %3D

Q: Q.2. If 7, 1, and r, be the roots of 2x +5x-330, then find: (a) E (b) Er

A: For given cubic equation first, we will find the roots of equation. so we will get real and complex…

Q: Determine the value of k that satisfies the following identity (x is a variable). In(kxa-b) = 2…

A: Determine the value of k

Q: 9. Let u = : (4, -1), v = (0, 5), and w = (-3, -3). Find the com- ponents of a. u + w c. 2(u - 5w)…

A: We have u=(4,-1)v=(0,5)w=(-3,-3)

Q: [1 ㅇ 1 Let A = 0 -1 %3D Lo ㅇ -1] a. Compute A² and A3. b. What is A1019

A:

Q: Please answer in typing format for like

A: Given : For two events A,B∈Ω,(i) P(B|Ac)= 0.1 (ii)P(Bc|A)= 0.8(iii)P(A)= 0.4Where Ω is the set of…

Q: Use z = a + bi and w = c + di to show that z + w =7 + W.

A: Consider a complex number z=a+bi Then, the complex conjugate of above complex number is given by:…

Q: -1 -2 -3 -41 1 2 3 Let A = 1 2.) Find adj (A)

A:

Q: Find the argument of 1+i ал with integer a,b b write your answer as a/b for Arg (1+i) =-

A: We have to find the argument of 1+i in the form of arg(1+i)=aπb with integer a, b.

Q: R² = gen gen

A: see below the reason

Q: 4. An ordinary differential equation is given as follows in the form of the initial value problem.…

A: Given - An ordinary differential equation is given as follows in the form of the initial value…

Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: To show that the group <a, b | a^5 = b^2 = e, ba = a^2b> is isomorphic to Z2, we need to…

Q: LET Z Z₂ = FIND ZI 리 Z₂ 8+31 9-21 AND Z₂ Z₂

A:

Q: -275 2. Let A 013 -135 Find the adjoint of A.

A:

Q: Suppose the multiplication cx is defined to produce (cx1, 0) instead of (cx1, cx2 ). With the usual…

A: The multiplication cx where x∈ℝ2 is defined as cx=cx1, 0 because x=x1, x2 where x1 and x2 belong to…

Q: Evaluate [R(5xy + z²)dV, where B = [-10, 10] × [0, 1] × [0, 10]

A:

Q: Which of the following is equal to da? In(x) + c +c 20 +0 с

A:

Q: 9. Which of the following is one of the possible answers when you integrate the expression 2csc² x?…

A:

Q: tan(z1) 0.9947 + 0.1462i 0.0364 1.0047i

A: The definition of tangent function for complex number is tanz=e2iz-1i(e2iz+1). Use 4-2i for z1 and…

Q: Solve the non-linear Differential Equation y"=-e xy = f(x) by explicitly following these steps:…

A: Use the following formulae, to obtain the solution.

Q: (+7.,(9-3) p ind G LD (+) t S+1+ひ!S

A:

Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

A:

Q: Show that if we make the change of variables =x – ct and n =x + ct, then, as in (16.7), a?u ,a²u a…

A:

Q: What is the difference between the minor of an element aij and the cofactor of the element?

A:

Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: We have to show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.