Let H be the set of points in the second quadrant in the plane V=R^2. That is, H = { (x,y) | x ≤ 0, y ≥ 0 }. Is H a subspace of the vector space V? does H contain the zero vector V? is H closed under addition? is H closed under scalar multiplication?

Q: Let W = {a + bx + cx2 + dx c- 3d = 0} be a subspace of Pg. Then th dimension of W is equal to %3D O…

A: ANSWER :

Q: Show that [0, ∞) and (0, 0) ad subspaces of R with the usual topology are not homeomorphic.

A:

Q: In the vector space , with the Euclidean inner product (i.e. the dot product), consider the subspace…

A: The fourth option '2' is correct. First find the dimension of W. Write the four vectors that span W…

Q: Find the projection of the vector v onto the subspace S. S = span 1 %3D V = 1 -1 1

A:

Q: snip

A: The given equation is the parabolic equation                    y = x2

Q: Find the orthogonal projection of u on the subspace of R³ spanned by the vectors v₁ and v₂. u = (1,…

A:

Q: 5. Find basis for the subspace u- of R for the vector u (1,3, -4). (Here u- means %3D orthogonal…

A:

Q: Is R? a subspace of the complex vector space C²2?

A:

Q: a) Let V be the set of all polynomials of degree 2. Is Va subspace of P, the vector space of all…

A: If two vectors are in subspace then their sum should also belong to subspace

Q: Find the projection of the vector v onto the subspace S. 8. 4 S span 23/2 9. projs V = 11/2

A: Find the projection of vector V.

Q: Find the projection of the vector v onto the subspace S. S = span

A:

Q: Let R be the field of real numbers. Then {(x,2y,3z): x, y, z ER}is a subspace of R°(R) ?

A:

Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 1 -1 1 -1 1 1 1 [1] 1 II…

A:

Q: Find the projection of the vector v onto the subspace S. 1 1 1 S = span 1 v = projs v =

A:

Q: .a. Is the set of vectors W = {(x,y,z) x,y,z € R,x=z+2} subspace of R³?

A: Given that a) W=x,y,z|x,y,z∈ℝ,x=z+2 of ℝ3. b) W=pt-tq of M22 Check the space W is the subspace of…

Q: if a vector space is the set of real valued continuous functions over R , then show that the set W…

A: Given V is a vector space of all continuous functions over ℝ. W is a set of differential equation…

Q: 1. Find the ortho gonal puojection of the Vector (1,3,1 on the subspace of IR? Spanned by…

A: Projection

Q: Let W be the subspace of the space of all continuous real- valued functions spanned by {cos2 t,sin2…

A: let U= cos2t,sin2t,cos2t and W be the subspace of all continuous real-valued functions spanned by…

Q: Let W is a finite dimensional subspace of an inner product space V and y is any vector in V. The…

A: Let W be a finite dimensional subspace of an inner product space V. Let T be an orthogonal…

Q: The span of a set of vectors from a vector space V is a subspace of V. true or false?

A:

Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors ui

A:

Q: Find the projection of the vector v onto the subspace S. 1. S = span v = projs v =

A:

Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

Q: Explain why the set of vectors V vector subspace of R2 = {[+] -1} ist :x>0, y> -1 is NOT a

A: Given: set of vectors  V=xy:x≥0,y≥-1 Explain why the set of given vectors is not a vector subspace…

Q: Find the projection of the vector v onto the subspace S. S= span projs v =

A: Any linear subspace is a combination of many subspaces, these subspace may distinguish with each…

Q: Let (V,(*,*)) be an F-inner product space,where F is either R or C. LetU C V be a subspace and let a…

A:

Q: Find the dimension of the subspace of all vectors in R° whose second and fourth entries are equal.…

A:

Q: Provide a situation in where it shows a union of two subspaces of a vector space V and is not…

A:

Q: Suppose W is a subspace of Rn spanned by n nonzero orthogonal vectors. Explain why W = Rn.

A:

Q: Find a basis for the subspace given by the plane −3x + 2y + 5z = 0.

A: we have to find a basis for the subspace given by −3x +2y + 5z = 0.

Q: ) Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: First we need to write given vectors in matrix form and try to use row reduced echelon form(RREF) :

Q: 2 Find the orthogonal projection of u = onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

A:

Q: Find the projection of the vector v onto the subspace S. S = span 2 projs v = %3D

A:

Q: Is the set of functions (taken from a vector space consisting of all functions of the real numbers):…

A:

Q: (1, 2, 3, 4, 6) and let W be the subspace of R° spanned by {u1, u2}, where u1 (1, 2, 1, 2, 1) and uz…

A:

Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

Q: Find the orthogonal projection of u = 1 onto the subspace of R³ spanned by the vectors - 3 2 V1 =…

A:

Q: 4. Consider the vector space RR of functions f: R R. Let U = {f: R → R: f(42)=0}. Show that U is a…

A:

Q: 5. Find basis for the subspace u- of R for the vector u = orthogonal subspace of u) (1,3,-4). (Here…

A: As we know that S=v1,v2,...vk be a set of vectors in Rn  then S is called an Orthogonal if and only…

Q: .Is the set of all vectors of the form b. where a and b are any real numbers, a subspace W of R?…

A: Yes, W is a subspace of R^3.

Q: Let u, = u2 = -1. and uz =0| Note that u, and uz are orthogonal but that uz is not orthogonal to…

A: Introduction: If two vectors are perpendicular to one other, they are said to be orthogonal. The dot…

Q: If B is basis for (x, t) then By = {BnY/BE basis for the subspace topology Ty on y IS 9

A:

Q: Find the orthogonal projection of u = 1 onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

A:

Q: Let f be a function in C[-T, 1] with inner product (f,g) = Sf(x)g(x)dx and W be a subspace spanned…

A:

Q: 4. Find the distance from the vector j = to the subspace on R³ spanned by { 19: | }

A:

Q: Let ui = (1, –2, – 1), u2 = (2, 2, -2), and v = (0,0, 1). v is not in the subspace W spanned by u,…

A:

Q: Let R be the field of real numbers. Then {(x,y,z): x,y,z are rational numbers } is a subspace of…

A:

Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors ui

A: Given:   v = 123 , u1 = 2-21 , u2 = -114    Also, given that the subspace W is spanned by the…

Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors u;. are orthogonal.)…

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.