2) One of the following subsets of IR2 is not subspace: a) S = {, xeR} b) s = {], = x3} %3D %3D e) s = {, * X1 = 2x2} -2x3) d) S = %3D

Q: 1. Is W=set of upper triangular 3 x 3 matrices a subspace of V=all 3 x 3 matrices? Support your…

A: I have showed that any two vectors form W linear combination of these also lies on W

Q: Suppose U, W,, W, are subspaces of a vector space V. Show that (Un W,) + (UnW,)Cun (W, + W,) Find…

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Q: Is the union of two subspaces of a vector space, a subspace.

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Q: Find the dimension of the subspace H of IR2 spanned by the vectors and

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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: Let v1=[ 1 0 −1 ], v2=[ 2 1

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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: Why are [0,1] and (0,1] which are subspaces of the real number system with the usual topology not…

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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: Find a basis for the subspace of R4 spanned by S.S = { (6, −3, 6, 34), (3, −2, 3, 19), (8, 3, −9,…

A: Given: S = { (6, −3, 6, 34), (3, −2, 3, 19), (8, 3, −9, 6), (−2, 0, 6, −5)} To find: Basis spanned…

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = -197 1 -13 10 5 8-6…

A:

Q: Suppose that S is a subspace in R spanned by all solutions to -x,+3x,3D0. Then its orthogonal…

A: See the detailed solution below.

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, 9, -2, 53), (-4, 2, 4, –2), (8, –4, –8,…

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Q: If V is direct sum of two subspaces, then every vector in V has .representation

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Q: Find the orthogonal projection of 5 16 onto the subspace W of R spanned by 4 -4 and 24 projw (7)

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Q: ate be two Subspaces fram Rs ver Ehe field IR Final wiAWe

A: Answer

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: Show that the solution vectors of a consistent non-homogeneous system of m equations in n unknowns…

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Q: Sketch all four subspaces associated to mat 1 2 A = 3 6

A: Respected student, By Bartleby guidelines we have solved all the four subspaces with the first…

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: The set of all nxn matrices whose entries are odd integers is a subspace of Mnn. Is it true or…

A: A subset of a vector space is a subspace if it is a vector space itself. First of all the space…

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

A: Let S=3, 1, 1, 3, -2, -1, -1, -3, 4, 2, 1, 3, -12, -6, -3, -8

Q: suppose subspace L of R that expand by collection 4 の> find angle between vector 2 and subspace L.

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Q: Find the dimension of the subspace of all vectors in R° whose second and fourth entries are equal.…

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Q: Provide a situation in where it shows a union of two subspaces of a vector space V and is not…

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

A: The solution is given as

Q: that set of of degree subspace of P₂ Prove or disprove all Spolynomials is 43 not? Or

A: P2 is vector space of real polynomial of degree less or equal to 2. That is P2=px=a0+a1x+a2x2:…

Q: Is the set of noninvertible 2 × 2 matrices a subspace of R2×2 ?

A: Given, ℝ2×2=abcd: a,b,c,d∈ℝ Let M be the set of all 2×2 noninvertible matrices  i.e.…

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

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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: Compute the projection of (1, 1, 1) onto the subspace generated by (0, 1, 0) and (-4, 1, 3)". Record…

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Q: Give example of subspaces of land l?wich are not closed.

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Q: pan(1,1 – x, 1 +x², 2x – 3) = span(2, 2 – x°, 2x² – x, x + 1). - %3D - -

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Q: Find the orthogonal projection of onto the subspace W of Rª spanned by projw() = v= 4 -2 -13] 3 15…

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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: Find a basis for the subspace of R3 spanned by S.S = {(2, 3, −1), (1, 3, −9), (0, 1, 5)}

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Q: Show that (4, 14, 8) lies in the subspace of R generated by (-1, 3, 1) and (4, 1, 2). (4, 14, 8) =…

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Q: determine the dimension of the subspace of R3 spanned by the given vectors.

A: Determine the dimension of the subspace of ℝ3 spanned by the given vectors.

Q: Show that Null Space of Ax = 0 is a subspace.

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

A:

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

A: We have to find the basis.

Q: Why are [0,∞) and (0,∞) which are subspaces of the real number system with the usual topology not…

A:

Q: Let A e Mnxn and W be the set of all solutions for the homogenous linear system AX = 0. Prove or…

A: Given, A∈Mn×n and W be the set of all solutions for the homogenous linear system AX=0. We have to…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.