Find the dimen sion of the; H= Sp {l,0,1,2),(1,4, -3,-), (-1, 2, 1, 0) , (5 ,-7 -?,3){ subspare in the R" ond denote one bosis.

Q: Suppose U and W are subspaces of V such that dimU=4, dimW=5, and dimV=7. Find the possible…

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Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, –3, -2), (-2, –3, 2, -5), (1, 3, –2,…

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Q: What is the dimension of the subspace or the space of 5 x 5 matrices (ai) sucn that a11 +...+ az5 =…

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Q: 個同 . Find a basis for the Subspace W of R spanned by S What is the dimension of W?

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Q: Suppose that you wish to find the projection of u = (3,0,6)" onto the subspace W of R spanned by (2,…

A: We will find out the required solution.

Q: Find a basis for the subspace of R3 spanned by s. S = {(1, 5, 9), (-1, 6, 9), (2, 6, 1)}

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Q: Consider the following subspaces of R3: U=span[(2, 1, 1), (1, 2, 0)] W=span[(0, 2, 1), (0, 1, 2)]…

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Q: Find a basis for the subspace of Rº spanned by S. S = {(1, 3, 5), (-1, 4, 5), (2, 4, 1)} %3D

A: Answer

Q: Suppose W,, W2,. (a) span (W, W2 (b) If S; spans W; for i = 1,...,r, then S, US, U...US, spans W, +…

A: (a) W1+W2W1+W2 would be W2W2. Below is the justification.  x+y∈W1+W2,wx+y∈W1+W2where x∈W1x∈W1 and…

Q: of R". SICSZ, Show that Juppose that s, and Sz are subspaces. With the thet property, dim (s.)s dim…

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Q: Find a basis for the subspace of Rª spanned by S. S = {(29, –14, 6, –12), (-14, 7, –3, 6), (4, –2,…

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Q: Find a basis for the subspace of R* spanned by S. S = {(-11, -6, -4, -8), (-6, -3, -2, -4), (4, 2,…

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Q: Find a basis for the subspace of R* spanned by S. S = {(-20, –7, 2, –4), (21, 7, –2, 4), (-9, –3, 1,…

A: We have given set of vectors ,  S = -20 , -7 , 2 , -4 , 21 , 7 , -2 , 4 , -9 , -3 , 1 , -2 , -18 ,…

Q: Given the subspace W of Rt spanned by S = {(1,2, –1,0), (2, 2, 0, 1), (1,1, –1,0), (3, 5, -1,1)} •…

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Q: Find a basis for the subspace of R* spanned by S. S = {(43, -21, 6, 12), (-14, 7, -2, –4), (6, –3,…

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Q: Find a basis for the subspace of R* spanned by S. S = {(2, 5, -3, -2), (-2, –3, 2, –5), (1, 3, -2,…

A: The given set,S=2,5,-3,-2, -2,-3,2,-5, 1,3,-2,2, -1,-5,3,5

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, -3, -4), (-2, –3, 2, -5), (1, 3, –2,…

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Q: 4. Let S be the subspace of P₂ defined by S = span{1-x, 1+x, 5, 1-x², 2x}. Find dim (S), and show…

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Q: 1. Find the ortho gonal puojection of the Vector (1,3,1 on the subspace of IR? Spanned by…

A: Projection

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 9, -2, 53), (-5, 2, 5, –2), (8, –5, –8,…

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Q: Consider the following subspaces of R3: U=span[(2, 1, 1), (1, 2, 0)] W=span[(0, 2, 1), (0, 1, 2)]…

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Q: Find a basis for the subspace of R4 spanned by S. S = {(-11, 6, 4, 8), (-6, 3, 2, 4), (-2, 1, 1, 2),…

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Q: Which of the centroid(s) are trivial

A: Note that : A region if is symmetric about y-axis then x-coordinate of the centroid of the region is…

Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 4, 7), (-1, 5, 7), (2, 5, 1)}

A: The matrix form the vectors is: A=1-12455771

Q: Find a basis for the subspace of R3 spanned by S. S = {(5, 9, 9), (1, 2, 2), (1, 1, 1)}

A: To find the basis for the subspace of R3 spanned by the given set of vectors S.

Q: 4. Find an orthonormal basis for W+, where W is the subspace of R' spanned by the vectors (-1,…

A: To find- Find an orthonormal basis for W⊥, where W is the subspace of ℝ4 spanned by the vectors -1,…

Q: Find a basis for the subspace of R* spanned by S. S = {(64, -21, 9, 27), (-21, 7, -3, -9), (6, -2,…

A: B is called the basis for the subspace of ℝ4 spanned by S  if i) B is linearly independent  ii) B…

Q: Use the Gram-Schmidt process to construct an orthonormal basis B for the subspace W of Rª spanned by…

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Q: Show that [0, 1] and (0, 1] as subspaces of R with the usual topology are not homeomorphic.

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Q: Find a basis for the subspace of R4 spanned by S. S = {(3, 9, –3, 53), (-4, 3, 4, –3), (8, –4, –8,…

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Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0, 3), (2, 1, –2), (0, – 1, 8),…

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Q: Find a basis for the subspace of R* spanned by S. S = {(5, 9, –5, 53), (-3, 5, 3, -5), (8, –3, –8,…

A: A matrix being in row echelon form means that Gaussian elimination has operated on the rows, and…

Q: Show that [0,1] and (0,1] as subspaces of R with the usual topology are not homeomorphic.

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Q: Find a basis for the subspace of R³ spanned by S. S= {(4,2,-1), (1,2,8), (0,1,2)}

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Q: 3 3 -1 A=| 1 3 1

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Q: (1, 2, 3, 4, 6) and let W be the subspace of R° spanned by {u1, u2}, where u1 (1, 2, 1, 2, 1) and uz…

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Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, –3, -2), (-2, –3, 2, –5), (1, 3, -2,…

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Q: Find a basis for the subspace of R4 spanned by S. S = {(3, -2, -3, 6), (2, –2, –3, 6), (-1, 1, 1,…

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Q: 4. Let S be the subspace of P2 defined by S = span{1-x, 1+x, 5, 1-x², 2x}. Find dim(S), and show how…

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Q: Find a basis for the subspace of R4 spanned by S. S = {(3, 9, -3, 53), (-5, 3, 5, -3), (8, -5, -8,…

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Q: Find the orthogonal projection of 10 onto the subspace W of R° spanned by 9. and 3 -1-10 3 projw (i)…

A: To find  The orthogonal projection of v onto the subspace of W spanned by the given vectors.

Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0,3), (2, 1, –2), (0, – 1,8), (7,2,…

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Q: Find a basis for the subspace of R4 spanned by S. S= {(5, 9, -5, 53), (-2, 5, 2, -5), (8, -2, -8,…

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Q: Find a basis for the subspace of R" spanned by S. S = {(43, -21, 6, 18), (-14, 7, -2, -6), (6, –3,…

A: Subspace of  ℝ4  spanned by S is               S = { (43,-21,6,18) ,(-14,7,-2,-6) ,…

Q: Find a basis for the subspace of Rª spanned by S. S = {(2, 5, –3, –5), (-2, –3, 2, –2), (1, 3, –2,…

A: This question related to linear algebra's topic basis of vector space.

Q: 2 Use the G-S frocess ov thonarmal balis IR, spamid by: 466.11,(2,2,02, (0,0,1), (62,3)Ì find…

A: Here we use Gram Smidth Orthogonaligation.

Q: Find a basis for the subspace of R4 spanned by S.S = { (2, 9, −2, 53), (−3, 2, 3, −2), (8, −3, −8,…

A: To Find a basis for the subspace of  R4 spanned by S.…

Q: Find a basis for the subspace of R“ spanned by S. S = {(2, 5, –3, –5), (-2, –3, 2, –2), (1, 3, -2,…

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Q: The set of all nxn matrices having trace equal to zero. is a subspace W of Mnxn(F). Find a basis for…

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Q: Find a basis for the subspace of R* spanned by S. S = {(2, 5, -3, -3), (-2, –3, 2, –2), (1, 3, –2,…

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