Let W be the set of all vectors in R² With second component equal to twice the first, that all vectors of the form (9,20) (a) Use the Test for a Subspace to show that W is a subspace of R². (6) Using the x-y plane to represent R² make a sketch of W.

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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

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Q: 2. Determine whether the following sets with the corresponding vector addi- tion and scalar…

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Q: 2. How can you build a subspace of a vector space V by using a single vector vEV

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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

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A: The given vectors are                                   -3110, -12613, 3-55-6, -33-23…

Q: Let ?1 = (4 3 2 1), ?2 = (−2 0 -1 0), ?3 = (0 3 0 1) a) Find the subspace of R^4 spanned by these…

A: Note: There are many long answer for subparts in the questions. So I will answer the first two…

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Q: Let U and V be the subset of R' defined as U = { (a,b.c,d) : 3b-2d-a = 0 } and / = { (a,b,c,d) : a=c…

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Q: 1 5 0 2 4₂ -2, 1 Note that u₁ and u₂ are orthogonal. It can be shown that u3 is not in the 1 1 0…

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Q: Find the orthogonal projection of ✓ = projw(u) = 61 90 904 45 281 30 52 45 8-60 onto the subspace W…

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Q: 21 3 Find a basis for the subspace of R³ consisting of all vectors 22 such that 61 - 7x2 - 4x3 = 0.…

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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 ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

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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: Now try to find the projection matrix that will project vectors onto the subspace of R³ spanned by…

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Q: 1. Let v, = (43 2 1), v, = (-2 0 -1 0), v3 = (0 3 0 1) a) Find the subspace of R* spanned by these…

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Q: Let V be a vector space and W₁, W2 be subspaces of V. Then verify that W₁ + W₂ = {w₁ + W₂ : W₁ € W₁…

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Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

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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: 21 Find a basis for the subspace of R³ consisting of all vectors 2 such that -81 + 9x2 + 4x3 = 0 13…

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Q: Let I2 E R 21 = 13 + #4, D2 = #3 – 14 13 14 Show that V is a subspace of R“. Find a basis for V and…

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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: