III. SUBSPACES 2. Which of the following subsets of R* are subspaces of R¹? b. W={(a,b,c,d)| c=a+2b,d=a − 3b }

Q: Let H = {[ 21 12 x1, x2 € R 1,2 Show whether or not H is a subspace of R3.

A: We satisfy the clouser and scaler multiplication and show that 0 vector is also in H so H is a…

Q: (1) Consider the space M2×2 (R) of 2 x 2 matrices equipped with the usual addition and scalar…

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Q: Part: b:Let W be the set of all vectors of the form shown below in parts į and ii. In each part,…

A: A non empty subset W of a vector space V is said to be a subspace of V is:1. for all u, v ∈W we…

Q: Which of the following is a subspace of R? O A. All vectors of the form (a, 0,0). O B. All vectors…

A: Subspace of a vector space:  A subset V of ℝn is said to be a subspace of ℝn if 1. The zero vector…

Q: 1. Determine whether the set S is a subspace of V or not, where Explain your answer. S = {p(x) = P₁…

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Q: а. W- : x is a scalar |2x + y b. W = : x, y are scalars x + y c. W = +1 : x is a scalar

A: we have to check subspace.

Q: Please go through each option with explanation

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Q: Which of these are linear subspaces? :2x +3y=D0}in R? :xy: A. Is a linear subspace ):v = 1– x}in R?…

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Q: Let W be the subspace of R4 spanned by S V₂ = (1, 1, 1, −1), Let V₁ =(2, 1, 2, 1), W₁ = (1, 1, 0,…

A: (a) S={v1=(2,1,2,1) , v2=(1,1,1,−1) , v3=(5,3,5,1) , v4=(−1,−2,−1,4)}Subspace W spanned by S.A…

Q: Let V be a vector space of dimension 8. How many subspaces out of V can you make? A. 2 subspaces B.…

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Q: Determine whether U is a subspace of R³. U = {(2r, –s²,t)lr,s, and t E R}

A: Vector Subspace Test: A non-empty subset W of a vector space V is a vector subspace of V if and only…

Q: The set of points where y = -4. The set of points where x = -5. Subspace of R2 Not a subspace of R²…

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Q: II. Determine if the set S spans R³. If the set does not span R³, then give a geometric description…

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Q: 15 Suppose U is a subspace of V. What is U + U?

A: Let V be a vector space and U be it's subspace. Then , for all u,v ∈ U  u+v∈U and  cu ∈ U ,where c…

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

A: Let S is a 2D subspace of ℝ3 projs<2,-1,1>=<0.5,0.5,1> So consider the 2-D plane given…

Q: If W is a subspace, then ||projwv||² + ||v – projwv||2 = ||v|?.

A: Given W is a subspace of a vector space V. Now projWv denotes the projection of vector v onto the…

Q: Find all values of h such that vector y will be in the subspace of R spanned by vectors 3. V1, V2,…

A: we will first find the equivalent matrix and then reduce it to row echelon form

Q: Recall that lines through the origin are subspaces of R². 2x and W₂ is the line y = If W₁ is the…

A: Given, W1 is the line y=2x and W2 is the line y=-3x ,we have to find which statements are true about…

Q: 2. Let V = E3 and W = {x|x = a(1,0,2) + b(1,-1,3)} and S = {x\x = (x1,x2, 1)} where a and b are any…

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Q: The set {(x,3): x is in R)} is a subspace of R2

A: The given set is x,3: x is in R. It is known that any subspace should contain identity element.

Q: Which of the following sets are subspaces of R°? A. ((x, y, z) | x < y < z} B. ((x, y, z) | 5x – 9y…

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Q: suppose subspace L of R that expand by collection 4 の> find angle between vector 2 and subspace L.

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Q: 5. Let U = {(u1, U2, U3) E R3³|u₁ + u2u3 = 0} and V = {(v₁, V2, V3) E R³|v1 - 302 +503 = 0}. (a)…

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Q: how that if T is a linear operator on V and W1, W2 are T-invariant subspaces of V, en W1+ W2 is a…

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Q: 1. Which of the following sets constitute a subspace of R2? Why or why not? Illustrate each set,…

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Q: Which of the following subsets of R* are subspaces of R*? b. W = {(a,b,c,d)| c=a+2b, d=a-3b}

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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: a b a b M22 space of a, b, c e R and K= 20 - Which of the sets is a subspace under standard…

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