(11) Let p 1. Show that L [a, b] C LPla,b).

Q: Let L be the line in R2 through the points [:] } Find a linear functional f and a real number d such…

A: First, we will find the equation of a line given two points.

Q: Assume that A and B are nonempty, bounded above, and satisfy B CACR. Show that sup B < sup A.

A: Introduction: The supremum and infimum properties are the very important properties of any subset of…

Q: 4. (a) Let A € R² be open and let f: AR be C². Let (a, b) A and suppose the rectangle R= [a, a +h] x…

A: (a) Since f, using Mean value theroem w.r.t. x for two variables there exists a pR such that f(a +…

Q: Let A = ū= [¹²3] a [¹3] and v u= LO [2] and define T: R² → R² by T(x) = Ax. Find the images under…

A: The given matrix  and the linear transformation .The aim is to find the images of  and .

Q: Suppose that the translation T is described by (?,?)→(?+2,?−1)(x,y)→(x+2,y−1). What translation…

A: We have to find the translation described in x,y→x+2,y-1.

Q: 4. Show whether or not f is bijective. Letf : R → R_be defined as f(x) = I피+1 %3D

A: A function f is said to bijective if it is one-one and onto

Q: Q6. Let f : R? → R² be a function defined by f(t, s) = (1+3t, 2s – t).

A:

Q: Show that in R with the usual topology, the only open sets connected by trajectories are the open…

A: Given that R with the usual topology  A collection of of subsets of R which can be expressed as a…

Q: Suppose that A,B⊂S such that Pr[A|B]=25, Pr[A]=12 and Pr[B′]=12. What is Pr[B|A′]?

A:

Q: Forz € C, define the linear operator T₂ : C → C by T₂(w) = W. Characterize those z for which Tz,…

A:

Q: Exercise 4.4.5. Let A and B be sets. Prove that there is a bijective function f: A × B → BXA.

A: A and B are two sets.  We need to prove there is a bijective function            f : A × B → B × A.

Q: 3. Show that is a closed subset of R². {(x, y) = R²: y = x²}

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Q: . Let a := V1+ v3. Find the minimal polynomial of a over Q.

A:

Q: Let h : C N x N where C CZ given by h(m) = (m2 +1, m2 + 2). Choose all subsets C' such that h is an…

A:

Q: Let f = u + iv be analytic in the connected open set and assume u and v satisfy u? + 3v2 = 4. Show f…

A: