If x is in W, then x is orthogonal to some vector in a subspace W

Q: Show that the set W : {(x, y, 5x-4y)| x and y are real numbers} is a subspace of R³.

A: We are give, W=x,y,5x-4y| x and y are real numbers To show: W is a subspace of R3 This can be done…

Q: Show that W is a subspace of R¹.

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Q: Suppose that U and V are both subspaces of R . Prove that their intersection U ∩ V = {v : v ∈ U…

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Q: let S be the collection of vector [x] (3x1 matrix) in R3 that satisfy the given…

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Q: Let S = E M2x2; a = d and b +c = 0} be a subspace of M2x2- Then the dimension of S is equal to: 1 4

A: S=abcd∈M2×2; a=d and b+c=0 be a subspace of M2×2

Q: If S is a subspace of R", then so is the orthogonal complement of S.

A:

Q: Find a basis for the subspace of P2 spanned by the given vectors.  1 + x, x2, -2 + 2x2, -3x

A: Basis are (1, 1,0), (0, 0,1), (-2, 0,2), (0, -3, 0)

Q: Let U and V be subspaces of a vector space W. Prove that their intersection U∩V is also a subspace…

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Q: Determine is Question 2 whether W = W = {(a; z { (a; 2; 6) | α; 6ER} subspace of R

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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…

A: We write y = p+o, where  is the projection of y, on W and o = y −p is orthogonal to W Since  are…

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…

A: In this question, the concept of the Orthogonal Decomposition theorem is applied. The vector…

Q: If V is a linear subspace of R", and x1 , ×2 , ... , Xn E V, then we must have span {x1, X2, Xn} =V.…

A: To determine that the statement, if V is a linear subspace of ℝn and x1, x2,....,xn∈V, then spanx1,…

Q: If a subspace of V of R contains the standard vectors ei, e2, eg, then V must be R. True False

A: We will show that V is a subset of R³. Then, we can claim that, V = R³

Q: Let W be the subspace of all symmetric matrices in M2,2. What is the dimension of W?

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Q: Prove that the subspaces of R3 are {0}, R3 itself, and any line or plane passing through the origin.

A: Let S be a subspace for R3   Hence,              If S is the subspace then by definition:…

Q: Determine whether the set A= (x,y,z):x+y%3D3Z is a subspace of R or not?

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Q: Show that if Z subspace of a space Y and Y is a subspace of a space X then Z is a subspace of a…

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Q: Let W be a subspace spanned by the u's, an

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

Q: Suppose V is finite-dimensional and U and W are subspaces of V with W^0 ⊂ U^0. Prove that U ⊂ W.

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Q: If S and T are subspaces of V, then SUT is a subspace. Select one: True False

A: Given S and T are two subspacewe have to check whether S∪T  is subspace or notClearly  S∪T  is…

Q: Find all values of h such that vector y will be in the subspace of R spanned by vectors 3. V1, V2,…

A: we will first find the equivalent matrix and then reduce it to row echelon form

Q: Suppose U and W are two-dimensional subspaces of R3. Show that U∩W≠{0}

A: We want to show that  U∩W≠{0}

Q: Let W be the set of all 3 x 3 matrices whose trace is zero. Show that S is a subspace of M33.

A: Let W be the set of all 3×3 matrices whose trace is zero. Show that W is a subspace of M33.

Q: Let W be a subset of the vectors in R where W = X2 X4 -x3 = x, - x, }. Show that W is a X3 3. X4…

A: We will use the formal definition of a subspace of a vector space to prove that, W is a subspace of…

Q: Prove that if S1 and S2 are orthogonal subspacesof Rn, then their intersection consists of only the…

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Q: The set {(x,3): x is in R)} is a subspace of R2

A: The given set is x,3: x is in R. It is known that any subspace should contain identity element.

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: Let W be the set of all the vectors of the form y where x and y are any real numbers. 2х-Зу…

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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: Show that if Z subspace of a space Y and Y is a subspace of a space X then Z is a subspace of a…

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Q: Show that the set W = {(x1, 0, x3): x1 and x3 are real numbers} is a subspace of R3 with the…

A: Given: the set W = {(x1, 0, x3): x1 and x3 are real numbers} is a subspace of R3 with the standard…

Q: Let W be the subspace of IR' spanned by the vectors 1 4 -2 and -1 -7 Find the matrix A of the…

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Q: If W is a subspace of R" and ax is in W, where a is a nonzero scalar and x is in R". Then x is in W/…

A: We have to check

Q: If W is a subspace of R" and if u is in both W and w then u must be a zero vector.

A: I am going to solve the given problem by using the orthogonal property of a vector.

Q: Suppose the set {u,v} forms a basis for a subspace w in Rn. Let x=u+v and y=u-v. Show that {x,y} is…

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Q: If V is any three-dimensional subspace of R°, then V has infinitely many bases.

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Q: he zero vector in U is a subspace of V.

A: Inroduction a. Zero vector is a subspace of every vector space.

Q: If X is an inner product space, and A is subspace of X then A = A+ True False

A: Let A be a subspace of an inner product space X. Then (i) A⊥ is a subspace of X ; (ii) A∩ A⊥ = (0);…

Q: If v is in R°, then the set of vectors a with v x a = 0 is a subspace.

A:

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…

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

Q: Determine whether the given set SS is a subspace of the vector space V.    (2,3,4,5)

A: For subspace test , if u and v is any element of S then au+v must be in S where a is any scalar

Q: Find the distance from the point x = (1, 5, –4) of R³ to the subspace W consisting of all vectors of…

A: First we will find out the orthogonal basis for the subspace W. Then we calculate the orthogonal…

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…

A: Given vectors are y=466−1, u1=1101, u2=−120−1 and u3=−1011. Now, the formula of orthogonal…

Q: Let V be the vector space of symmetric 2 x 2 matrices and W be the subspace -4 -3 3 W = span{ -3…

A: There are so many vectors does no belong to W but belong to V.

Q: Is the set M={1/n | n ε z+} compact as a subspace of R?

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Q: Determine: if W = the set of all vectors in R2 whose components are integers is a subspace.

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Q: Determine: if W = the set of all vectors in R^2 whose second component is the square of the first.…

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Q: Prove that the intersection W n U of two subspaces of a vector space V is a subspace of V and prove…

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Q: If V is a 13 dimensional subspace of R20 then the dimension of V- must be

A: Definition of Orthogonal Complements Let V be a subspace of ℝn. Its orthogonal complement is the…

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.