1. Let A = (ai)nxn be symmetric and positive definite. Show that a) a>0, i=1,2,...,n. b) |a|<(a¡a„)³, i, j=1,2,...,n.

Q: 45. Let g(x) = [x]. Find a) g-¹({0}). c) g-¹({x|0<x< 1}). b) g-¹({-1, 0, 1)).

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Q: 13. Let U be the set of real numbers, A = {x |x is a solution of x - 1 = 0}, and B ={-1, 4}.…

A: Let's find.

Q: A statistics teacher wants to determine whether there is a linear relationship between high school…

A: Here n = 23

Q: Let p, q, and r be real numbers such that p + q +r = 26 and '/p + lq + '/, = 31. What is the value…

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Q: Prove that AAB = (AU B) - (An B),

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Q: Let yk = k", where n is a positive integer; then Ak" = (k + 1)" – k" - (1.112) nk"-+ n kn-2 +...+ 2.…

A: We have to solve given problem:

Q: C) If an expression is given that A+A'B'C=A+B'C, find the minimal expression of the function F =…

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Q: Prove that Vn > 0: 2º + 21 + .…+ 2" = 2n+1 – 1. ... an+1_1 Prove that Vn > 0: aº + a² + .….+ a" =…

A: Here, the objective is to prove the following: 1) 20+21+22+......+2n=2n+1-1   ; n≥02)…

Q: Show that Sn is solvable when n ≤ 4.

A: Given: Sn. We have to show that Sn is solvable when n≤4.

Q: Prove that for a # -1, a>0,n EN IS (1+a)^ n >=1+na.

A: Here let A=(1+a)n, a≠-1, a&gt;0, n∈N and B=1+na

Q: Let x, y be real numbers such that xy=1x and x≠y. Prove that x^2+y^2≥2\sqrt{2}|x−y|.

A: Given: xy=1x,x≠y To find: x2+y2≥22x-y

Q: (B1>0 (g) If a > b and c> d, then a + c > b + d. h) If a > b> 0 and c > d > 0, then ac > bd. i) If a…

A: For (f) ,We use a theorem that "if n∈ℤ and n≠0 then n2&gt;0.

Q: Find ||uLy|| in Figure u= (3, 5) = (8, 2) P. FIGURE

A: v=(8,2) u=(3,5) uv=?

Q: For each statement, either prove that it is true or come up with a counter example N(ATA) = N(A) ● •…

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Q: Find the interval of En=o 2"(z – 3)" O (3.5, 0) O (2.5, 0) O (2.5, 3.5) O (2, 3)

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Q: Let Z~ N(0, 1). Find P( - 2.4 < Z < 0.9). Submit Question

A: Solution-: In this case, Z is the standard normal random variable with μ=0 and σ=1. Mathematically,…

Q: f6) = 5-31 5+3x Q11. Let %3D

A: Given: To Find:

Q: Find the interval of En=0 2" (z – 3)" O (2.5, 3.5) O (2, 3) ( (3.5, 0) O(2.5, 0)

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Q: Is Q closed over multiplication? (Y/N)

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Q: E. On the right: a. r*ak + r*(-ak) = r*(ak + (-ak)) b. r*(ak + (-ak)) = r*0 c. r*0 = 0 F. So, r*(aj…

A: the last three lines also proves b and c too.

Q: Let G = (a, b | a² = b² = (ab)?). a. Express b²abab³ in the form b'a'. b. Express b'abab³a in the…

A: Given: The expression is G=a,b|a2=b2=(ab)2. To Express: (a) The expression b2abab3 in the form of…

Q: Assume that M= N(h)+ k, h² + k, hª+ .... Use the following data to find N, N,(h) = 2.451,…

A: Let, M=Nh+k1h2+k2h4+. . . . And also given that, N1h=2.451, N1h2=2.896, N1h4=3.285, N1h8=3.786,…

Q: Provide an interpretation which is true and one that is false. (∃ x)(P(x,b))

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Q: Compute only one the inverse z-transform of 02 a) X(z) = 5)X(z) = Q3 ROGIZ| >3- ROC Z > 3 %3D %3D…

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Q: a) Р(X > х) %3D 0.5. X = i b) Р(Х > х) %3D 0.95. = X i с) Р(х < X < 9) — 0.2. X = i

A: GivenMean(μ)=9standard devaition(σ)=2

Q: 1. Let A=(a)xn be symmetric and positive definite. Show that a) a>0, i=1,2,...,n. |a|< (aa)², i,…

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Q: f (x) = { 0 S 1 if x is rational if x is irrational at any point x. (b) f(x) = (sin x)/x at x = 0.…

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Q: Let u= and v= identify 3u+v???

A: We have to identify 3u+v for the given vectors: u=2, -3 and v=4, -1. Finding 3u: 32, -3=6, -3

Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: Let u (41, U2, Uz). Explain why u•u > 0. When is u•u 0?

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Q: Let f1, f2, .. fn be n real-valued, differentiable functions.- Prove that e :[fif2 ... fn] = (fif2…

A: We have to prove that the given formula.

Q: 3) Let f(x) = 1 + 3x on [-8, 2]. Find the number c that satisfies the mean value theorem. a) O C= b)…

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Q: 2. Show that if a]b then a'|b² for all integers a and b (Symbols V, 3, A, V, V,A,→,-)

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Q: 4x-3=8 identifying terms of 'x)' c) Vanable d) operotor a) coefficient b) constan

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Q: Let Z ~ N(0, 1). Find P(Z > 1).

A: Z~N(0,1). This implies that Z is a Standard Normal Random Variable. The PDF of Z is given by,

Q: Ifx+y+z= 1 and x, y, z are positive, then show that ( 1)² ( 1)² ( 1)² 100

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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…