6. Let = {An: n = 1, 2, 3,...} where An = {0, 1, 2,..., n}. Find Un and nn. Prove your conjecture.

Q: b.) Show that if a and b are positive integers where a is even and b is odd, then (a,b) = (a/2, b).…

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Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

Q: If u and are the vectors below, find the vector w whose tail is at the point halfway from the tip of…

A:

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: = Let a, b, and d be positive integers. Prove that if (a, b) : divides a, then (d, b) = 1.

A: Definition of gcd (a, b) =1 is a and b does not have common prime divisor. Using this we can easily…

Q: Ex2:] If S:= {1/n - 1/m:n, mEN3, find inf Sand sup S.

A:

Q: 4. [7.4 & 7.5] If... a = i +3j - 2k, and b=i-3j-k, and c=2i+j-k, then... a) Determine (ā- 2b) b)…

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Q: Suppose s and t are distinct natural numbers. Show that lcm(s, t) + lcm(s+1, t+1) > 2st/(sqr(|s −…

A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)>2sts-t

Q: antip . Prove that 4" -3"-7 is a multiple of 84 for each positive even m.

A:

Q: Let u (9, 9, 8) and = (-9, -1, - 8). = Find proj, (u). -

A:

Q: Haw:2 ExPress the Sumef the Vectars Aß and E ,if ACl,-), B (2,0)_, C(-1,)_ and D(-2,2).

A: Here is the solution

Q: (b) Let a.. and m be positive integers. Prove that if (a,m) = (b, m) = 1, then (ab, m) = 1.

A: Given  a, b and m are positive integers.  (a, m) = (b, m) = 1.We have to prove that (ab, m) = 1.

Q: Let u == (7,5,-5) and = (−1, −2, 2). Compute the following: u v . . = 2 7(ū. v) = (7) · v = ū. (77)…

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Q: If (R – {0}, .) = (Q,.) then 1=0 1=-1 -1=0

A: For the given statement

Q: (1) and (.), (.) dz = Find the number of terms in where z = gu, v/ and u

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: = (-10,6, –4) be in R and a be in R. Then , 36 , Let x ат — ).

A:

Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

A: The given matrix is: A=-300010-180-2 Reduce the matrix to identity matrix form by performing…

Q: . Show that sup{3 – 2 : n = 1,2, ...} = 3. %3D

A:

Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              => k(15 - 13) = 2k for any integer k              => 15 k -…

Q: Given: f(t) = 3t4 + 6. Evaluate: F(3) Use 2 decimal places. 2.30

A: Here we have to apply laplace transform.

Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

A:

Q: 10. Prove that 7/2 TC/2- sin 0 cos (cos a cosec 8) de -0 2 (1-cos a).

A:

Q: A loan of $39,999.55 is to be repaid by payments at the end of each quarter for eight years. Each…

A: The given details: Principal amount, P=$39,999.55 Rate of interest, r=4%=0.04 Number of years,…

Q: 0 5. 21 ) Let A=[¹²] and B= [¹ Find AB. 13

A: Given query is to find Matrix product.

Q: Prove that du Inlul + C where n= -1 u

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Q: Q. One of the following statements is wrong: a. [-1,0] = [-1, 2] b.(1, 2] = [2,3) c. (-0,0) = (0.00)…

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Q: • Find the two values oft such that 99% of the area under the t-distribution is centered around the…

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Q: I find B such that AB = C. If 5 0 3 A = 2 01 9. C = 3 5 c- (* :)

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Q: Find the value of n(A U B) if n(A) = 8, n(B) = 13 and n(An B)=4. n(AUB) = (Type a whole number.)

A: