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.

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…

A: .

Q: (a) Give examples of three distinct vectors v1, v2, v3 in the vector space R3 such that v2 E…

A: Let v1 = {1,1,1}v2 = {2,3,4}v3 = {1,2,3} Here v2 = {2,3,4} = {1,1,1}+{1,2,3} = v1+v3

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

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Q: Determine the element of V that represents the zero vector 0 (i.e., determine the “value” of 0 in V…

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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

Q: Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 1, O),…

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Q: a. Write the solution set to the following equation in parametric vector form (consider ₁ to be the…

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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…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Let the set U = b:c = a = R3 be given. Then which of the following statement or statements are…

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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: A line l passes through the point P(2,4, 3) and is parallel to the vector (3, 2, –3). | At what…

A: Proceed as shown below

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: 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: Let V1, V2, V3 be vectors in R³ given by 1 »-(;) · ~ -(:). = 6 V2 = 2 2 0 The set {V1, V2, V3} is…

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Q: 2- Concisely describe what the following terms mean for a set of vectors and how we quickly check…

A: Define: 1. Collinear vectors 2. Coplanar vectors 3. Linearly independent vectors 4. Linearly…

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: In the following exercises, determine whether the subset H of the vector space V is a subspace…

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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: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given, A=( 1,1,0 ); B=( -2,3,-4 ); P=( -3,1,6 )To find: Distance from point P to the line through A…

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: Let $K$ is a horizontal shear, next draw a vector $\vec{x}=\left[\begin{array}{l}x_1 \\…

A: Let be the transfomation representing vertical shear of the vector  .Then we have The above can be…

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

A: Concept:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: V = M ₂x2 (IR) let M = { A€ V A = A} N = {A = V A = - A^²} Subset of the vector space V The answer V…

A: To prove  V=M⊕N we need to prove  (i) V=M+N and  (ii) M∩N=0