Let N (A) A = = span 4 5 -6 -2 -2 6 2 -4 - 10 –7 6 2 Find a spanning set for the null space of A. -4 4 - 3 18

Q: Show that R has the same cardinality as the interval (–2, 2) by building a bijection between the two…

A: This is a problem of Real Analysis and Topology.

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

A:

Q: What topology does one get on the real line if one imposes both the left and right Sorgenfrey…

A:

Q: Q7(a)- State and prove Cantor’s Intersection Theorem. (b)-verify Q7(a). with real life example.

A:

Q: Consider the partial order with domain{3,5,6,7,10,14,20,30,60}and with x ≤ y if x evenly divides y.…

A:

Q: Elaborate on the role of duality in topological spaces.

A: Introduction:Topology is a branch of mathematics that studies the properties of spaces and the…

Q: what is reflexive Banach space ?

A: Banach space: A normed linear space N,· is called banach space if it is complete metric space. A…

Q: Let Find a spanning set for the null space of A. 6 - [º A = 3 3 -2 -3] 2

A:

Q: Prove that the set A = {x ∈ R | 3x + 2 ≤ 0} has a maximum

A:

Q: Give examples of three relationships that show all possible combinations of minimum and maximum…

A: We need to give examples of three relationships that show all possible combinations of minimum and…

Q: Determine the dimension of the span of each set. 6 3 12 - A = span ({0}) 2 - -1 4 20 10 40 dim (A) =…

A: Here sets A,B and C are given. We find dim(A),dim(B) and dim(C).

Q: etermine whether the set of x-2x²,2+5x-x²x+x²} is linerly independent in P

A: First we use definition of linearly independent Set and we check given vectors are linearly…

Q: Consider the partial order with domain {3,5,6,7,10,14,20,30,60} and with x ≤ y if x evenly dividesy.…

A:

Q: 6.) Let A = {small, medium, large, extra large}, B = {purple, C= {t-shirt, polo, hoodie}. a. List 2…

A: Definition : A×B×C=a,b,c|a∈A,b∈B,c∈C We have  A={small, medium, large, extra large} B={purple, gold}…

Q: 2. Let A = [1,3], B = {5}, and C = [4,6]. Write the inequalities (or equalities) that specify each…

A:

Q: Is a R a maximal deal

A: No, it is not necessarily true that aR is a maximal ideal in a commutative ring R with unity. In…

Q: Given that V = {v₁ = [-5 1 1], v₂ = [5 5 3], v3 = [-15 3 3], v4 = [1 2 m]}. Find m such that V is…

A: ℝ3 is a 3 dimensional space. If V={v1,v2,v3,v4} contains a linearly independent set of cardinality…

Q: Explain with an example of a topological space which is singleton that is open but not close and…

A: Example in refer of not  open but closed .Take , Here A is singletone set which is closed but not…

Q: Find and prove the minimum possible value of…

A: p + q + r + s >_ 4( pqrs )1/4 for all positive integers p, q, r and s.

Q: the shabilty of the following systems (Consider Hhe quadrake form as lya punov system.) Ms. *- X-x…

A: Lyapunov stability theorem is applied to determine the system is asymptotically stable nearby the…

Q: Let P(x; y) : x plays in y A(x) : x is athletic. S(x) : x is smart.  E(y) : y is in English…

A:

Q: Let A = {2,6}. Consider the set B = A x P(A) (where P(A) is the power set of A). Define a partial…

A:

Q: 1.10 For each map, give the chain of range spaces and the chain of null spaces, and the generalized…

A: For each map, we will be giving the chain of range spaces and the chain of null spaces, and the…

Q: when can two spanning sets be equal?

A: See solution below

Q: List the elements for the given sets {x|x is a perfect square FROM 1 to 10} {x|x is an integer…

A: Set: A well-defined collection of different objects. For example: Set of natural numbers= {1, 2, 3,…

Q: (ii) Determine supremum and the infimum of the set A=(0,10)∩R∪[−2,8]A=(0,10)∩R∪[−2,8] if they exist

A: It is assumed that R denotes the set of real numbers.

Q: Suppose that U and V are finite sets with |U| = m and |V| = are the maximum and minimum possible…

A: Maximum and minimum values of the set

Q: Suppose A and B are nonvoid, bounded, disjoint subsets of R. Mark all of the properties that must be…

A: Answer given below.

Q: df. Every nonempty proper subset of R is either open or closed.

A: False

Q: {x, x + 1, x2 + x + 2, x2 + x + 1} a spanning set for P3?

A:

Q: Provide examples of sets A and B where strict inequality sup(A+B) < sup A+ sup B holds.

A: We have to given an example to prove given inequality:

Q: If X = {u,v} what is the power set of X? (in answering this question, use {} as the null set, and do…

A:

Q: *· Given a set (x, x+3, x+6, x+9, x+12} where xE2*, show there exists at minimum 1 of the numbers in…

A: Given set is x,x+3,x+6,x+9,x+12 where x∈ℤ+ The objective is to show that there exists at minimum 1…

Q: 9. 2 -6 - 72 Is 9. in the null space of - 5 9. 1 -5 - 36 Select an answer > Next Question 6.

A: Null space of a matrix A consists of all the vectors B such that ;

Q: Consider the "divides" relation on the set A = {1, 2, 3, 5, 6, 7, 8, 10, 20, 30, 60, 70} (a) Draw…

A: A Hassen diagram is a graphical representation of the relation of elements of a partially ordered…

Q: This question examines your understanding of spaces of polynomials and their bases. Please tick all…

A: Note: As per guidelines, I can do only three subparts of a question

Q: 5) Let R be a binary relation over the positive integers defined as follows: R = {(a, b) | 2b < a <…

A: