Let V=R^2 and let H be the subset of V of all points on the line 2x+3y=6. Is H a subspace of the vector space V? does H contain the zero vector V? is H closed under addition? is H closed under scalar multiplication?

Q: Show that [0, ∞) and (0, 0) ad subspaces of R with the usual topology are not homeomorphic.

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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

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A: The given equation is the parabolic equation                    y = x2

Q: a 2. Is the set of vectors of the form a subspace of R? Show your proof

A: **As per our guidelines we are allowed to answer only one question at a time. Kindly please re-post…

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 v1=[ 1 0 −1 ], v2=[ 2 1

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

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Q: Find the distance of the point (1, 7, -9) in R from the subspace of vectors of the form (a, 8a, b).

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Q: Find the standard matrix for the orthogonal projection of R3 onto the subspace spanned by aj=(1,1)…

A: The vectors that span the subspace are a1=1, 1 and a2=0, 1. The normalising vectors are 12, 12 and…

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: Let W be the subspace spanned by the vectors (1,2, 0, 3) and (2, 1,3,0). Find : a basis for W+.

A: Given that W is a subspace spanned by the vectors 1 , 2 , 0 , 3 and 2 , 1 , 3 , 0 . i.e., W = span1…

Q: |Find basis for the set of vectors in R²on the line y = nx. where n is last digit of your arid…

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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: Find a basis for the subspace of R3 spanned by

A: In this question, we find the basis for the span of subspace S. S={(-1,2,5),(3,03), (5,1,8)}

Q: 5.4) (6)  Find the projection of the vector v onto the subspace S. S = span 0 1 1 , 1 1 0 v = 3…

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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: Let Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R³ spanned by…

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Q: Find the projection of the vector v onto the subspace S. 1 1 1 S = span 1 v = projs v =

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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: Show that the set of vectors {(−4, 1, 3), (5, 1, 6), (6, 0, 2)} does not span R3, but that it does…

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Q: Find a basis for the subspace of R" spanned by the vectors 1 1 .2. -3. .6.

A: Use the given vectors.

Q: Let S be the set of all 2 × 2 real matrices given by   Find 2 × 2 matrices X, Y, Z such that S =…

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Q: Find a basis of the subspace of R* that consists of all vectors perpendicular to both and -2 Basis:

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Q: Let ū be some fixed vector in R" and let S be the set of all vectors in R" that are orthogonal to ū.…

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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: 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: Find the projection of the vector v onto the subspace S. S= span projs v =

A: Any linear subspace is a combination of many subspaces, these subspace may distinguish with each…

Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

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

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Q: Find the orthogonal projection ŷ of y = 6 onto the subspace 2 -3 W = Span { ui = 3 Ex: 1.23

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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: ) Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: First we need to write given vectors in matrix form and try to use row reduced echelon form(RREF) :

Q: 2 Find the orthogonal projection of u = onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

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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: Find the projection of the vector v onto the subspace S. S = span 2 projs v = %3D

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Q: Find the projection of the vector v onto the subspace S. -1 1 -1 S = span v = -1 |-2/3 -2/3 projs v…

A: To find the projection of the vector v onto the subspace S, where

Q: rthonormal basis of the subspace spanned by the vectors is

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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: 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 u = 1 onto the subspace of R³ spanned by the vectors - 3 2 V1 =…

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

A: As we know that S=v1,v2,...vk be a set of vectors in Rn  then S is called an Orthogonal if and only…

Q: .Is the set of all vectors of the form b. where a and b are any real numbers, a subspace W of R?…

A: Yes, W is a subspace of R^3.

Q: Construct an orthonormal basis for the subspace of R spanned by the vectors (1, 2, 3, -1), (2, 0,…

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Q: Find the orthogonal projection of u = 1 onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

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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: Let ui = (1, –2, – 1), u2 = (2, 2, -2), and v = (0,0, 1). v is not in the subspace W spanned by u,…

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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.

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.