can a subspace of R^n have a dimension less than n.

Q: Show that a finite union of compact subspaces is compact.

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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: If the system Ax = b is inconsistent, then b must have a component in which fundamental subspace of…

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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: , find the orthogonal projection matrix on the subspace defined by the equation: 2х-у-3z-0.

A: a) Let v1 = [3,6,0] and v2 = [0,3,-1] be two vectors on the plane As we have 2(3)-6+3(0) = 6-6+0 =0…

Q: Find a basis for the subspace of Rª spanned by S. S = {(2, 9, -2, 53), (-4, 2, 4, –2), (8, –4, -8,…

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Q: Please define the four fundamental subspaces? Please have your answer types.

A: Suppose that A is a m -by- n matrix that maps vectors in R^n to vectors in R^m. The four fundamental…

Q: 5. Show that {(1,-1,2,-3), (1,1,2,0), (3,-1,6,-6)} and {(1,0,1,0), (0,2,0,3)} do not span the same…

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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: A subspace always contains the zero vector.

A: True Because of subspace is a nonempty set.

Q: What is a linear subspace?

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Q: (() 2 6. Are the two subspaces span and span (() orthogonal? Justify your answer.

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Give two examples of infinite dimension vector spaces.

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Q: what is the smallest subspace containing the vectors u, v and w? what is the span of a set of…

A: Span is the all possible linear combination

Q: Explain the term Vectors that Span a Subspace.

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Q: Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1) (2) On the plane…

A: (1) Let a→=6,0,0, b→=1,2,1 Then orthogonal projection of a→ along the vector b→ is a→·b→b→·b→b→…

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: The set of all 2X2 matrices with ones on it's main diagonal is a subspace of R2x2 . true or false

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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: 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: Find an orthonormal basis for the subspace spanned by (0,1,2), (-1,0,1) and (-1,1,3).

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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: Let C2(-∞,∞)={f(x) in C(-∞,∞)|f''(x) exists for all x} be the set of differential functions. Show…

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Q: Show that a subspace of a Hausdorff space is Hausdorff.

A: Prove that, a subspace of a Hausdorff space is Hausdorff.

Q: Explain why the set of vectors V vector subspace of R2 = {[+] -1} ist :x>0, y> -1 is NOT a

A: Given: set of vectors  V=xy:x≥0,y≥-1 Explain why the set of given vectors is not a vector subspace…

Q: Is W=set of upper triangular 3 x 3 matrices a subspace of V=all 3 x 3 matrices?

A: In this question we need to check W is a subspace. so we need to check two properties * w1 and w2…

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: Find a basis for the subspace spanned by the given vectors. 3 Span 3 -1,2 1 3 4

A: The given subspace consist of all vectors in Span-231, 3-12, 123, -154. Take S=-231, 3-12, 123,…

Q: The set { n > 1} is closed in (0, 0) as a subspace of R. - True - False I know the answer is true…

A: Given set  1nn≥1

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: 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: 8) Describe geometrically all subspaces of R" for n 1, 2, 3.

A: We will do this for all three parts; n = 1, 2, and 3 (in as clear handwriting as possible)

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: Please create/ give an example of a square hermitian matrix. Use Gram-schmidt process to solve the…

A: We have to give an example of a square hermitian matrix. Use the Gram-Schmidt process to solve the…

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

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

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Q: Find a linearly independent set of vectors that spans the same subspace of R as that spanned by the…

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Q: Define Vector Space and Vector subspace with the help of real time examples?

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Q: What is the dimension of the subspace 0 2 3 1 H = x1 x2 x3 X4 ER¹ : 2x1 3x2 + 4x3 5x4 = 0 ?

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

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Q: is a subspace of M23-

A: A nonempty subset W is a subspace of a vector space V if, whenever w1, w2 are elements of W and α is…

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.