Let H be the set of points inside and on the unit circle in the xy-plane. That is, let {{]***a :x² + y? < 1} Find a specific example-two vectors or a vector and a scalar-to show that H is H = not a subspace of R2

Q: a) Find all values of a so that polynomials f = 4t-a and g = 5t-6 are linearly dependent in P₁.…

A: We can find the value of 'a' for which the given polynomial is linear dependent.

Q: 3. Show that the set W = {(x, 0) : x e R} is a subspace of R?.

A: In order to show W is a subspace of R2 , we need to prove W is closed under addition. For any two…

Q: Answer the following: A SIAII OT VOITOUG 4. Determine if the odd functions (f(-x) = -f(x)) are a…

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Q: 6. Let Vi and V2 be subspaces of R" such that Vi C V2. Show that any vector v E R" can be uniquely…

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Q: If v1 and v2 are in R" and H=Gen{v1, v2}, then H is a subspace of R" Justify

A: Given that : and are in  Let Now, we  have to recall  the definition of subspace of a…

Q: Please go through each option with explanation

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Q: Show if W is a subspace of the vector space X, then W is convex.

A: Definition used: A set K in a vector space V is called convex if and only if  x, y belongs to K,…

Q: Decide if the two subspaces U = span(U) and V = span(V) spanned by the two subsets and of vectors in…

A: (.)   Orthogonal subspace :  Two subspaces 'U' and  'V' are orthogonal to each other if  u , v= 0…

Q: Let S be the space of all complex vectors (x, y, z) such that y = z². Determine whether or not S is…

A: In the given problem we verify the properties of vector addition

Q: 1. Determine whether w - {[:]•r:a-4-0} X1 E R? : : x1 – 23 = X2 is a subspace of R?.

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Q: 4 1 Let V= { X= (X₁₂X²)X₁9X4) ER" : X₁ = a X₁ +bx++exs} Where as boc, are fixed real number show…

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Q: Determine whether W is a subspace of V

A: Determine whether W is a subspace of V

Q: a Q#01:- Let W be the set of all vectors in R3 of the form where a and La + b! b are any real…

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Q: . Consider M₂ (R) as a vector space and its subspaces U₁= {A € M₂(R): A¹ = A} and U₂ = {A € M₂(R) :…

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Q: Let U be a subspace of a finite-dimensional Prove that dim(U) = dim(V) if and only if U = V. vector…

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Q: Let S be a 2D subspace of R. Find projs if projs =

A: Let S is a 2D subspace of ℝ3 projs&lt;2,-1,1&gt;=&lt;0.5,0.5,1&gt; So consider the 2-D plane given…

Q: Let W be the subspace of R³ spanned by the vectors Find the matrix A of the orthogonal projection…

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Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y = 5 - 1 1 18 V₁ 1 - 2 - 1 3 V2…

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Q: 5 Suppose that u = 1 2 and v= 0 are vectors in R³. Determine the smallest 2 --- 2 subspace H of R³…

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Q: Prove that if U and V are subspaces of R" and U <V then V+<U+.

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Q: Show that the given set V is closed under addition and multiplication by scalars and is therefore a…

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Q: Let W be a subset of the vectors in R where W = X2 X4 -x3 = x, - x, }. Show that W is a X3 3. X4…

A: We will use the formal definition of a subspace of a vector space to prove that, W is a subspace of…

Q: Let H span {(-11,0, –5), (–3,0, –1), (–2,0, –1)}. A basis for the subspace H C R³ is { vector

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Q: 2t 6. Let H be the set of all vectors Show that H is a subspace of R³. What is the -t dimension of…

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Q: Show that the set W={(x,y,1)|x and y are real} is not subspace of R3.

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Q: If T: R R´is a linear transformation such that 1 -4 T. .T -3 1 0. -3 and T 0 = 0. -2 4 then T 4 -1…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Consider the following two sets of Euclidean vectors: X U = -------- 7x²y + 2 wz=0 W X W = W…

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Q: S� is a set of vectors in a vector space V�, then SpanS is a subspace of V�. Please show that this…

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Q: Show that the given set V is closed under addition and multiplication by scalars and is therefore a…

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