Question: 4) Which of the following is a subspace of R^3? Justify your answer. i) W={(x,y,z)|x+y+z=0} ii) W={(x,y,z)|x^2+y^2+z^2=0} iii) W={(x,y,z)|x>0} iv). W={(x,2x,3x)|x is a real number}

Q: Let v1 vector=[−4  h] and v2 vector =[−10   20]   (check image for reference) Then span(v1…

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Q: V4. Consider the following two sets of Euclidean vectors: 3x + 2 y + 4 z = 0 y? + 3 x = 3 z Explain…

A: The solution is given as

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 - V1, V1 + V2,…

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Q: Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is…

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Q: Let v = [2 10. (a) How many vectors does Span {v} contain? (b) List a few vectors in Span {v} and…

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Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

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Q: Use the function to find the image of v and the preimage of w. T(Vy. V2) = ( V2, 2v1 - v2), v = (7,…

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Q: Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W. Show that V ∩W…

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Q: Verify that V5 is a subspace of RS

A: Please check step 2 for solution.!

Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

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Q: ^2

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Q: How did you get the vectors and to get a cross product for a perpendicular vector to i+j and j+k.

A: How did you get the vectors <1,1,0> and <0,1,1> to get a cross product for a…

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

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Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: Find a linear map 7 that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

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Q: Which of the following sets of vectors spans R^2?  A. {(1, 1), (–2, –2)} B. {(1, 1), (1, 2)} C.…

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Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

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Q: V4. Consider the following two sets of Euclidean vectors: 3x + 2 y + 4 z : Y y? + 3x = 3 z Explain…

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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)…

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Q: Let U, W be subspaces of R" and assume UnW = {0„}. Prove that dim(U + W) = dim(U)+ dim(W). Here U +…

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Q: Consider the vectors v, V, V3, and b. 2. 4V2 4 V1 Vg 6 ,b 7 b = | [8 9.

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Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned by…

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Q: 3. Is the set of all vectors (x, y) in R2 with the usual addition and scalar multiplication, a…

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Q: Let U₁, U2, U3 – be the following subspaces of Rª U₁={a, b, c, d)=R4| ²b=c; a=d=0}; U2={(a, b, c,…

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Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: and .We have to find .