A = E M2x2(R), 2 3

Q: _If A = Verify that [A-!]" = [A"]¬1 ? l1 2.

A:

Q: Let i be a positive integer and A, [-i+ 1,1]. Then U14, %3D O R O None of these O F1,11

A: Given that 'i ' be a positive integer and Ai=-i+1,1. We have to find the union ∪i=1∞ Ai.

Q: Let a, b e Z. If both a and b are odd, then 5a+b is even and a+4b is odd.

A: Proof:  Given that a and b are odd Let a=2k+1 and b = 2m+1 for some  integers k, m  ∈Z Now,…

Q: Find U1 A, and N14; where: a. A = {-i, i} for every positive integer i. b. A = {i°, i', i?} for…

A:

Q: If A = (; A-: )-..R. e M2x 2(R), find A" for any positive integer n.

A:

Q: 6. Let r> 2 be an integer. Show that R(2r, 2r) > 2

A:

Q: Find the value(s) of such that х -1 2х 1 -1 0=12 2 -1 -x O x=4 or x= -3 O x= -4 or x = -3 O x= -4 or…

A:

Q: 1. Let H=10 so 100r f (r,b)=[?][?]+1006 . Compute a[2][?]f

A: we have to derivate the given function f(r,b)=100r1+100b .

Q: 1 fn is a positive integer, then (D -a) II

A:

Q: A factor (x − a)k, k > 1, yields a ________ ________ x = a of ________ k.

A: x=a is a repeated zero of multiplicity k, when we have (x-a)k.

Q: Z/mZz Zm

A: We need to prove that Z / mZ is isomorphic to Zm .

Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

A:

Q: M d formulas for the entries of M", where n is a positive integer.

A: To find the power of a matrix

Q: Q3- Find the numerical value of 6. xdz,if c = c, + c2 + C3.defined in the given figure. (2,2) (1,1)…

A: Given is∮c x dzalong C1equation of linex-12-1=y-11-1=tx=t+1   y=1dxdt=1   dydt=0∫c1f(x,y) ds=∫01…

Q: 4. Show that for all formulas p, p,0 E S(P), (a) (9 = 4) = ¬(4 ^ ¬ab).

A:

Q: Find all the numbers z such that e^2iz= 5i.

A: We are given : e2iz=5i Now Using  Euler's equation: ( eix=cos x+i sinx) ⇒e2iz=cos (2z) +i sin(2z)…

Q: (c) Let n be a positive integer and assume that there are integers a and b ab. Show that a < yn or b…

A:

Q: d x" = nx"-1 de 4. Prove that NɛQ

A: ddxxn=nxn-1 ;   n∈Q

Q: Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

A: Given quadratic equation is,

Q: 2. T = {m EZ| m 1+ (-1)^i, for some integer i} *

A: Given T=m∈ℤ|m=1+-1i for some integer i

Q: Consider a positive integer 1 < i < 9. Then, given T(n) = 2T([n / 2] + i) + n, show that T(n) E O(n…

A: Given: T(n)=2Tn2+i+n The positive integer 1≤i≤9

Q: Determine the numbers a such that x a (p) is solvable for p = 7, 11, and 13. %3D

A: Given, x3≡amod p At p=7 We know that suppose p is rational prime p≡1mod 3 then x3≡a mod p is…

Q: TRUE/FALSE If A = A−1, then A must be equal to either I or −I.

A:

Q: Remind yourself what () means. For this class, we will use the convention that () = 0 if n < k or if…

A:

Q: Develop a simple expression for the entries of An, wheren is a positive integer and

A: The given matrix is A=112012. Observe that pattern as follows.

Q: 4. For each positive integer i, let A, = {x € R| -<x < } = (-;;4) a. Find U-, A;. i=1 b. Find N 4:-…

A:

Q: nd all values of z for which zª + 2 – i2/3 = 0 and represent them geometrically. |

A: To solve the given equation by using D'Moivre theorem we find the point. The 4 value of z satisfy…

Q: Find the value of t for which 1 V3x+1 O none of the choices 6 O 3 O 5 O 4

A: Here, given that: ∫1t13x+1dx=43

Q: Which of the following is equivalent to 2x3 .x-1? A B D 5 NIN NIN inIN

A: The correct option is option (D)  The detailed solution is as follows below:

Q: prove the following : a) a0=0 b) (-a)v=a(-v)=-av c) av=0 implies either a=0 or v=0

A: What is Identity and Inverse Element: Identity element is that element which on performing binary…

Q: the value(s) of c such that 3c2n n=0

A: The given question is taken from the sequence and series in which we have to find the value of the c…

Q: Let n be a positive integer, then n+1≥ for all n.T/F

A: We need to show that n+1≥n for all n where n is a positive integer. Lets proof by contradiction

Q: Find all values c in (−64, 64) such that f '(c) = 0.

A: From given information, it can be predicted that f(-64) = 0 f(64) = 0 To Find : all values c in (64,…

Q: For any natural number m, evaluate 1/m +x")( 3m 2m 2m +x 2x +3x" +6)"* dx, x > 0. m X

A: Topic:- Integration

Q: Determine the value of x for which r || s. Then find mZ1 and m2. mz1 = 30 - 4x m22 =50 – 44x The…

A:

Q: H PROVE : กะ1 [-¹-², ¹+ ²] = [1,1] 1 t

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Let U = {x: x is an integer and 2 7}, B = {x: x² > 20}. ii. A = {x: x2 - 3x + 2 = 0}, B = {x:x + 7…

A: We have to determine which condition applies on set A and B.

Q: Let...

A: Given expansion formula is  a+bn=∑nkk=0nan-kbk

Q: Let M=( 3 Find formulas for the entries of M", where n is a positive integer. Mn = =

A:

Q: Let i be a positive integer and A, = [-i+1,1[. Then N14= %3D

A: We have to find the first intersection first.

Q: Let n be a positive integer and M %3D Then M"

A:

Q: a + b (2) (a) Prove by contrapositive : Va, b e R* : a < b → a <• (b) Prove by contradiction : For…

A: Part(a) We need to prove by contrapositive. In proof by contrapositive, if we have a statement "if p…

Q: Use the definition of e to show that for any real numbers 0, 01, and 02, a. "": = M0, +0,) b. e" =…

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Q: Let a, b e R with a < b. Assume that a + <b - for all n E N. Show that 1 = (a, b). a + ,b n n=1

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Q: The set of exhaustive values of m for which both roots of the equation x2 – 2mx+ m² – 1 = 0 are…

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Q: Find all values of x for which |6x – 1| = 1 – 6x. - Select one: O (-00, 1/6] O -1/6 not in the list…

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Q: A (T+ 7) = A·I+ A ·G A (c.F) = c · (A · T) Verify these two properties by direct computation in the…

A:

Q: Find all m, n E N such that: n! + 2n + 49 = m²

A: This problem can be solved by graphical approach. Use a graphing utility to plot the graph of…

Q: If (1 + i)(1-i) 2. a07879297 + 1. b17865173i. What is a + b? Your an swcr

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.