Verify that U1 = {(x, y) E R² : y = -2x} is a real vector subspace of R?. hat U2 = {(x,y, z) E R³ : y = x², z = x} is a D3

Q: Find one voctor in R' that spans the intersoction of U and W where U is the xy-plane-that is, U =…

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Q: 2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B = {1+x= 2x°, -1+a…

A: given B=1+x-2x2 , -1+x+x2 , 1-x+x2B'=1-3x+x2, 1-3x-2x2 , 1-2x+3x2 b) find the coordination matrices…

Q: Which one of the following is a subspace of the vector space M2 (R) of 2 x 2 matrices? ss (X) the…

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Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: 12): x € R. Is W a subspace of V? Expalin your 3x- Q1. Let V = R³ and W = answer? Q2. Show that M2x2…

A: The properties of subspaces: Closed under multiplication; Closed under addition; Contains the…

Q: Let L be the line in R³ that consists of all scalar multiples of the vector onto L. proje 22 T .…

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Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: What is the dimension of the vector space S=abc detEM2x3(R): a=b=c=0}

A: Dimension of vector space is number of element in basis

Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

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Q: Find a unit vector orthogonal to both u and v. u = 2i5j + 3k 2-3 V = + -k 10

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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-{ », :x, y, a, b e R and x - a = y – b}.Is W a subspace?

A: We will use the one step test for vector subspace to check if W is a subspace or not. We know that…

Q: 2s Let H be the set of all vectors of the form Find a vector v in R' such that H span {i}. -s S

A: Spanning set of H

Q: 5. Let ū = (-1,3, 2) and i = (1, 1, -1). Find all vectors x' that satisfy u x i = v.

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Q: 3. Let W C R be an inner product subspace with standard dot product. { 12 then If W I1- 2r2 + 4 = I3…

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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: Find the dimension of the subspace of all vectors in R'whose second and third entries are equal. O…

A: Dimension of subspace is 6. Since dimension of R^7 is 7 and the given subspace has second and third…

Q: Let V = R' and define vector addition as (x, y, z)+(x', y', z')= (x+x',y+y',z+z') (standard…

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Q: Mrs. Wigen conducted a survey in her math class. She asked each of her students to tell her how many…

A: The data plotting helps to visualize the relationship between variables. A dot plot consists data,…

Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

A: Given that                   y→=-4-3 and u→=66.

Q: Verify all vector space axioms under the given operations (x,y,z)+(x',y'z') = (x+x'+1,y+y'+2,z+z'+3)…

A: The objective of the question is to verify if the given operations satisfy all the axioms of a…

Q: Don't change the W subspace. It is  W = {(x,-x, 2x): x, y ≤ R}

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Q: Describe all extensions of the identity map of ℚ to an isomorphism mapping ℚ(3rd root of 2) onto a…

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Q: Let L be the line in R that consists of all scalar multiples of the vector 2 Find the orthogonal…

A: Concept:

Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R3 b)show that R' =…

A: Solution of the problem as follows

Q: Find a vector-valued function whose graph is the plane x+y+z= 12, O r(u, v)=-ui-vj+(12-u-v)k O r(u,…

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Q: Show that U = {Ae² sin(3x): A = R} is a subspace of V.

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