5. Let W be the set of all vectors p(t) in P2 such that p(0) = 0. Show that W is a subspace of P, and find a basis for W. %3D
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A: With the help of definition of projection of a vector on a subspace, we solve this problem.
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Q: 5. Let W be the set of all vectors p(t) in P, such that p(0) = 0. Show that W is a subspace of P,…
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Q: 1. Let V = (Z7)4, and let W = {(a, 2a, a + 2b, b + c)|a, b, c E Z7} |(a) Show that W is a subspace…
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A: Explanation of the answer is as follows
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A: The objective is to find orthogonal complement of W
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Q: Consider the following vector v ER and the subspace SCR¹. -0-000 S= = span V= V₂ (a) Find an…
A: consider the following vector v∈ℝ4 and the subspace S⊂ℝ4 where v=1234 and S=span1111, 01-11, 0110…
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Q: [5 Find the orthogonal projection ŷ of y = onto the subspace 3 W = Span { uį = 2 u2 3 Ex: 1.23 ŷ =
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Q: 4. Consider the following subspaces of P. H = Span{1+t, 1– t°} and G=Span{1+t+t°, t – t°, 1+ t+t®}…
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Q: (1) Suppose U and W are both five-dimensional subspaces of R°. Prove that UnW + {0}.
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A: Please check step 2 for the solution.!
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Q: 1. Let V = (Z;)ª, and let W = {(a, 2a, a + 2b, b + c)|a, b, c € Z7} |(a) Show that W is a subspace…
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Q: 5. Let W be the set of all vectors p(t) in P such that p(0) = 0. Show that W is a subspace of P and…
A: W be the set of all vectors p(t) in P2 such that p(0)=0.
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- Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many vectors are in a basis for the row space of A? c How many vectors are in a basis for the column space of A? d Which vector space Rk has the row space as a subspace? e Which vector space Rk has the column space as a subspace?Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
- In Exercises 1-4, let S be the collection of vectors in [xy]in2 that satisfy the given property. In each case either prove that S forms a subspace of 2 or give a counterexample to show that it does not. xy0Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
- Consider the vector spaces P0,P1,P2,...,Pn where Pk is the set of all polynomials of degree less than or equal to k, with standard operations. Show that if jk, then Pj is the subspace of Pk.In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn,WAinMnn:detA=1
- Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.