4) Suppose u, v E V, where V is an inner product space, and ||u|| = |||| = 1 and (u, v) = 1. Find u - v. 5) Suppose U and W are finite-dimensional subspaces of the inner product space V, with W CU+. Find Py Py. %3D

Q: What is the dimension of the subspace H of R spanned by the given ved V1, V2 and v3 2 3 Vị = -8 V2 =…

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Q: Consider the R-vector space V-R2. Which of the following subsets of V is a subspace? The line 2x+y=1…

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Q: 7 Given the inner product space (R³(R),+,·,· ), where xoy = 3x₁y₁ + 2(x₂Y₁ + X₁Y₂) + 3x₂Y/₂ + 2x3V3,…

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Q: Is the set V = {(x, y) x >0} where (x1, y₁) + (x2, Y₂) = (x₁x2, y₁ + y₂) and c (x, y) = (x,cy) a…

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Q: B 1 Find the dimension of the subspace V span{v1, v2, V3, v4} in R³ where vị = 2 1 V2 = , V3 = and…

A: We find dimension of the subspace V

Q: 2) suppose that w is a subspace of some vector space V. Let u be any vector in w and Let ✓ be a…

A: Let W be  a  subspace  of  a  vector space V over  a  field F.Then, orthogonal complement of W is…

Q: Let V be the vector space of continuous functions and the scalar product in V is defined as (f,9)=[…

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Q: Let V be an n-dimensional vector space. Define f: V→ R by f(v) = |v|". Let p,q E V.Find d fp(q).

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Q: of R". SICSZ, Show that Juppose that s, and Sz are subspaces. With the thet property, dim (s.)s dim…

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Q: W4 Pick any vector space V that you want, as long as dim(V) ≥ 6. Then, pick 4 vectors in the space,…

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Q: if u and y are vectors in a vector space and (u, v) is an inner product then which one of the…

A: If u¯ and v¯ are vectors in a vector space and ⟨u¯,v¯⟩ is an inner product.

Q: c) Mark each statement True or False. Justify the answer. A subspace is also a vector space. • R? is…

A: Here , A subspace is olso a vector space: it is true.  R^2 is a subspace of R^3 : it is false.

Q: 5. Let W be the subspace of the vector space V = R spanned by the vectors =(1,3, 1, -2), B = (-3,…

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Q: Show that the spaces (R,U) and (R,S) are Hausdorff.

A: Let a, b be any two distinct points of R so that a ≠ b

Q: Let V ((x,y): x 20) with standard operation on R2. Is V a vector space?

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Q: For what value(s) of the parameter p is the vector space described by the set of vectors {v1 = (-1,…

A: Approach to solving the question: Detailed explanation: Examples: Key references:…

Q: Which of the following choices is not a subspace of vector space R? a. (x,y,z):z=x-y b.…

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Q: 4B Given the Euclidean inner product space (regular) (R³(R),+,.,) and the vector subspace V = {(x,…

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Q: Let V be an n-dimensional vector space. Define f : V→R by f(v) =|v|². Let p, qe V. Find d fp(a).

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Q: Which of the following sets is not a vector subspace of p? OA. W = ((x,y)x = 2y} O B. W - ((x,y)y-…

A: Subspace of a vector space

Q: Let I2 and = in R', we have 43, () (u, v) uv:= x1y1 + 122 + 3Y3. Let ui = and Uz = Show that B =…

A: Since you have Posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Consider the vectors v1, v2, ..., Um in R". Is span (01,..., īm) necessarily a subspace of R" ?…

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Q: V 3 (R) is a vector space and W₁ = {(a, 0, c) : a, c = R} and W 2 = {(0, b, c) : b, c € are two…

A: Provided that V3 is three dimensional vector space over field Rand V has two W1 and W2 subspace…

Q: 2. Let H be the set of all vectors of the form claim. 2t 0. Is H a subspace of R³? Show your

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Q: (R, Ts) is a topological space and NC R , find the T. subspace topology.(T|N is the subspace…

A: Let ℝ, τs is a topological space and ℕ⊆ℝ Define τs|ℕ=ℕ∩A: A∈τs Then τs|ℕ is a topology on ℕ  (i) As…

Q: 1. Is the subset V {(x, y, z, w), y = 3z, w = 2x + 1) a subspace of R*? Show the details of %3D your…

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Q: Consider the set ? = ((x, x+ y, 2y)|x,y are real) of vectors in r3 . Is W a subspace? If yes, prove…

A: We have Set S = {(x, x + y, 2y) | x, y are real}. Let u, v be any two element of S then,

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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.