What is the topology on the subspace {(x,1/2)|0 < or equal x < or equal 1} of the space [0,1] x [0,1] with dictionary order topology on R^2

Q: (a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a, b, c) ER3 | a = 0, b = 3c}. (c) {(a+b, ab, 2a + b) | a, b R}…

A: (a), (b) , (c), (d)  are subspaces .

Q: Why is this set not a subspace of R^3? W = { (a1, a2, a3) : a22 = a1 - a3 } ( the two 2s are…

A:

Q: can a subspace of R^n have a dimension less than n.

A: Yes , it can be .

Q: Which of the following sets is not a subspace of the space R^3? (a) R^3. (b) Any plane passing…

A: Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: 1 0 Span 1 2 -3 N -2 -2 5 3 -2 2 9 3 I[s -2 4 0

A: The given spanning set in ℝ5is span10-12-3, -2-25-29, 0-2306, -1-2406. We have to find the dimension…

Q: Find the orthogonal projection of the subspace W spanned by 4 1 -5 -2 0 -2 -5 projw (7) = 1 -4 ;]}…

A:

Q: V = { (x1, x2, x3) E R^3 |x1 2 0, x2 + x3 = 5 } of the set R^3 a sub of Show whether it is a space.

A:

Q: Is it possible to solve it using words like claim as my professor did in his example in other photo?…

A:

Q: Show that ℓ^1 is a normed linear space.

A:

Q: Verify that V5 is a subspace of RS

A: Please check step 2 for solution.!

Q: W = (x:x= X1 X2 LX3 where x3 = 5x₁ + 8x2

A:

Q: True or False, S is a subspace of R 3 x1 (8] x2 x3 S = O True O False 2x1 + x3 = 0, x1 + x2 = x3 = 0…

A:

Q: Show that a finite union of compact subspaces of a topological spaces X is compact-

A: We have to show that the finite union of two compact subspaces of a topological space X is compact.

Q: Determine whether the given subset is subspace of R^3 W={(x1,x2,x3):x1+x2+x3=0}

A: Let the subset W is given as W={(x1,x2,x3)| x1+x2+x3=0} Determine whether the given subset is…

Q: V {(x1 , X2, X3 ) E R³ |x2 + x3 = 3} %3D nin R3'ün bir alt uzayı olup olmadığını gösteriniz.

A:

Q: )Let P3 be the vector space of all polynomials of degree 3 or less in the variable z. Let Pi (z)…

A: Given that P3 is the vector space of all polynomials in variable x of degree 3 or less.We have to…

Q: Let P3 is the vector space of polynomials of the degrees3,Consider the polynomials…

A: Given :  P3 is the vector space of polynomials of degree less than or equal to 3. To prove :  We…

Q: In linear algebra, a subspace of R^n can have a dimension less than n.  (True or False)

A: Given that the space and subspaces of the space. In general the subspace of every space have…

Q: Give example of subspaces of land l?wich are not closed.

A:

Q: Given the Euclidean inner product space (R³(R),+,,*), where for each x=(x1,x2,X3), y=(yı,y2,y3) ER³,…

A:

Q: Find the orthogonal projection of v= [15 8 0] onto the subspace V of R^3 spanned by [-1 -2 -2] and…

A:

Q: If p4 is a vector space formed by polynomials of degree less than 3 And  s = { ax^3 + bx^2 +cx + d…

A:

Q: There is no linear transformation T\colon \RR^5 \longrightarrow \RR^5 such that the range and kernel…

A:

Q: Which of the following subsets is not a vector subspace in the vector space R^3?

A:

Q: 12- Aşağıdakilerden hangisi R? vektör uzayının bir alt uzayı değildir? a) O W = {(-3a,2a): a e R}…

A:

Q: 3x-2y -2x + Y and V = {v(x, y) : x, y E R}. 1. Set v(x, y) = x + y

A:

Q: Define Vector Space and Vector subspace with the help of real time examples?

A:

Q: Find a basis for the two-dimensional subspace of R4 defined by Explain your reasoning. V := x= x1 2…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.