4. (a) Find a basis for the subspace H of R spanned by the following vectors: 00000 1 (b) What is the dimension of H?

Q: Let W be the subspace of IRª spanned by the vectors 4 2 and -1 Find the matrix A of the orthogonal…

A: Consider the given information: Let W be the subspace of ℝ4 spanned by vectors :1-11-1,4-2-1-7 To…

Q: 2. Let S be the subspace of R5 spanned by x = (1, , (a) Find a basis for S- (b) Give a geometrical…

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Q: 4. Consider the subspace V of R' given by 3 V = span (a) Find an orthonormal basis for the…

A: vector subspace  V  of  ℝ4  given by ,               V = span 1001 , 31-11 (.)  If  W be a subspace…

Q: 5. Show that if H and H2 are two orthogonal subspaces of H, then Hin H2 = {0}. Does the converse…

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Q: 5. Find basis for the subspace u- of R for the vector u (1,3, -4). (Here u- means %3D orthogonal…

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Q: Let 2 3 and : Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R°…

A: To use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R3 spanned by…

Q: Find a basis for the given subspace of R° , and state its dimension for the plane 4 x - 2 y + 5 z =…

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Q: 4 Let S be the subspace of R* spanned by x1 = (1,0, – 2, 1)" and x2 Find a basis for S. (0, 1, 3,…

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Q: 5. (а) Show that the formula ((: :) (; 3)) = xã + 2yỹ+ zž + 2wũ gives M2x2(R) the structure of an…

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Q: 1 Q5. Find an orthonormal basis of the subspace spanned by the vectors

A: The solution is given as

Q: Find the subspace spanned by the three vectors [2 3 1]T, [2 1-5]T, and [2 4 4]T Feuth

A: We will check the  vectors that it is linearly dependent or linearly independent.  If the vectors…

Q: Q5. Find an orthonormal basis of the subspace spanned by the vectors 1 3 3 121C

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Q: -2 an orthonormal basis of the subspace spanned by the vectors 121C

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Q: 1 2 Find a basis for subspace V of R4 spanned by the vectors 3 dimension of V? 8 What is the

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Q: Let 1 -3 and let W the subspace of R' spanned by u and v. Find a basis of W-, the orthogonal…

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Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 1 -1 1 -1 1 1 1 [1] 1 II…

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Q: 6. (a) Determine whether the set of all vectors of the form (a,b,c), where b a+c, is a subspace of…

A: The subspace of R3 is (a,b,c) where b=a+c

Q: (3) Suppose that V is a finite dimensional vector space over R and T € L(V) has no eigenvalues.…

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Q: Find a basis of the subspace of R* that consists of all vectors perpendicular to both 0. 1 and 6- 4.…

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Q: 2 Find the orthogonal projection ŷ of y = onto the subspace 3 -2 W = Span { ui u2 Ex: 1.23 ŷ =

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Q: Let S be a subspace of V. Starting with a basis {81,..., s} for S, how would you find a basis for…

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Q: Find the distance from the vector -1 y = -5 10 to the subspace W spanned by -2 1 u 0 and v= 2 ||

A: The given vector is y=-1-510 and the subspace is u=-200, v=12-1.

Q: Find a basis for the subspace given by the plane −3x + 2 y + 5z = 0.

A: Given that, -3x+2y+5z=0

Q: Suppose {x,y} is a basis for a subspace W of Rn. Let u = x + y and v = x − y. Show that {u,v} is…

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Q: {[:} 5. (a) Consider the subspace W = span and consider the vector -1 1 u = -1 |. Find the vector w…

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Q: 3) Find a basis for the subspace of Pz Censistiny of all vectors of the following properties f(tD,…

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Q: Find the orthogonal projection of onto the subspace W of R' spanned by -1 -1 -1 1 1 projw (7)

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Q: -2 Find an orthonormal basis of the subspace spanned by the vectors 3 1310

A: Given 3 vectors. We need to find an orthogonal basis of the subspace spanned by the given vectors.…

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

Q: 5 1 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = -7 3 Ex: 5 ||

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Q: Find a basis for the subspace of R3 spanned by S. S = {(1, 3, 6), (-1, 4, 6), (2, 4, 1)} EEE

A: Basis of subspace of ℝ3 i) It must be linearly independent. ii) Its span ℝ3

Q: 2. Consider the following vector v R¹ and the subspace SCR¹. S = span (a) Find an orthonormal basis…

A: Note:- As per our guidelines, we can answer first part of this problem as exactly one is not…

Q: 2, Find bases for the fundamental subspaces; R(A), R(A"), N(A), and N(A"), given the matrix 1 -2 2 A…

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Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

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Q: (11) Find a basis for the orthogonal complement of the subspace of R" spanned by the vectors V1 =…

A: We have to solve given problem;

Q: In C[−π, π], find the dimension of the subspace spanned by 1, cos 2x, cos2 x.

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Q: Find a basis for the subspace given by the plane −3x + 2y + 5z = 0.

A: we have to find a basis for the subspace given by −3x +2y + 5z = 0.

Q: 4) Find a basis for the subspace of R' spanned by the vectors. {(1,1,0,0), (0,0,1,1), (-2,0,2,2),…

A: We have fond the maximal linearly independent subset of the given set.

Q: 1 1 onto the subspace W = Span -7 Find the orthogonal projection ŷ of the vector y = u = 2 Ex: 5

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Q: Find the orthogonal projection of -13] 15 onto the subspace W of R4 spanned by 4 and 5 -2 -2…

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Q: 5. Let P2 be the vector space of polynomials of degree at most 2. Determine if the vector v = = 10x…

A: Consider the given vector v is in the given subspace. Consider the real numbers a, b such that the…

Q: 2 Find the dimension of the subspace H of R spanned by – 12 8 ..... dim H =

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Q: Show that the set of vectors of the form a +b forms a subspace of R³. Find a 2а — b basis for this…

A: Given set of vectors of the form: aa+b2a-b Let v1=a1a1+b12a1-b1 and v2=a2a2+b22a2-b2 be two…

Q: 4. Consider the subspace V of R' given by 1 3 V = span (a) Find an orthonormal basis for the…

A: Solution:-

Q: 6. (a) Determine whether the set of all vectors of the form (a,b,c), where b = a+c, is a subspace of…

A: To show the subset W is a subspace , we need to show that (a) 0∈W (b) For every w1 , w2∈W , we have…

Q: Find the orthogonal compliment of the subspace W of 2x2 upper triangular matrices in the vector…

A: Using standard inner product in the space of matrices.