Let n >= 3 be an integer. Let Vn(x) = {[x 1 1 1 ... 1 1]T,[1 x 1 1 ... 1 1]T, [1 1 x 1 ... 1 1]T, ... , [1 1 1 x ... 1 1]T, [1 1 1 1 ... x 1]T, [1 1  1 1 ... 1 x]T} be contained in Rn. (a) For what values of x does Vn(x) fail to be a basis for Rn? (b) For each such value of x found in (a), what is the dimension of span(Vn(x))?

Q: A function f is choice of x1 and x2 in I, with xi<x2, then f(x) <f(x2). on an interval I if, for any

A: we have to fill the given blank statement. Statement : A function f is ____________ on an interval I…

Q: Prove that ||A||1 = maxi<j<n{E#1 laij|}. i=1

A:

Q: Let > 0 and 6 > 0 be real numbers that satisfy e' (1+a+²) = eª (1+b+ 2 ) eb Prove or disprove that a…

A: Its given that a&gt;0 and b&gt;0. We have to prove or disprove that eb1+a+a22=ea1+b+b22 is satisfied…

Q: 12. For each n € N, define A, = [0, 1+] and B₁ = [0,1]. - =1 (a) Prove that U1A,, is an interval,…

A:

Q: 4. Let f: RR be a Lebesgue measurable function. Prove that there exists a Borel measurable function…

A:

Q: (b) Given the set S = [-1,1] and the function g: S→ R defined by g(x) = that g is one-to-one, and…

A: g is one to one because  For every x there is a different image in g(x) if x= -1 then it's image is…

Q: (2) The floor function is defined as a| = max{m e Z|m < x}. Effectively, the floor function is the…

A:

Q: The number of units in Z31[x]

A: See the solution below.

Q: Prove if equal to MPn (W) dx= 2" (n!)" (2n+)! that m is an integer

A:

Q: X x² + 1 Let f: RR be defined by f(x) = f is a Borel function. O f is not a measurable function. a.…

A:

Q: Compute |x| and [x]= for each of the values of x 17/4

A: We have to compute the values of | x | and [ x ] for x = 17/4.

Q: A function f is continuous on [-3, 5] and contains the points (-3, -4), (0, ƒ(0)), and (5, –3). If ƒ…

A:

Q: Prove directly from the definition that if X and Y are independent and f and g are measurable…

A: Solution: Given X and Y are independent and f and g are measurable function then we have to prove…

Q: Prove that P[X |Y ] = (P[Y | X] · P[X] ) / P[Y]

A: From the definition of conditional probability, for two events X when Y is given PX|Y=PX∩YPY

Q: ind the m<t

A: Given: m&lt;R=140 m&lt;S=80 Find: m&lt;T=?

Q: 1. Let a be a positive real number and n be a natural number. Define S = {x €R: x >0 and x" a?…

A:

Q: compute measuralle

A: [f&gt;t] is an inverse image of (t,infinity) That leads us to give an answer.

Q: 3. Give an example of a non-Lebesgue measurable function f: IR→ IR such that || is a measurable…

A:

Q: Let n > 2 be a natural number. Prove that there is no continuous function q : C → C such that…

A:

Q: Use the method of Laplace transforms to solve the given initial value problem. Here, D[x] and D[y]…

A: We have to solve the given system of differential equation using Laplace transform.

Q: x₁ + x₂ + +x. Prove that -x₁)(1+x₂)... (1+x) ≤1+S+ ... S² S³ + 2! 3! +...+ uS - n!

A:

Q: Which one of the following functions satisfies the hypotheses of Rolle's Theorem in the interval…

A:

Q: 2b. In R show that : || x - y || || x + y || ≤ 11x11 ² + 11y11²2² -(1

A:

Q: Let x = [1, -3, 2]T. Find ||x||₁, ||x|4, and ||×||∞·

A:

Q: Which of the following intervals will contain all of the function values of f (x) on the interval-4,…

A: We can solve it by cross check from given options  Let we select 0 from interval [-4,1] at x=0 f(0)…

Q: The floor function is defined as bxc = max{m ∈ Z | m ≤ x}. Effectively, the floor function is the…

A:

Q: determine L−1[F].

A: