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

Q: Let (X, F) be a space. Prove that a subspace of a subspace is a subspace of (X, F).

A: Here given X, I is a topological space.

Q: Let V be the vector space of symmetric 2 × 2 matrices and W be the subspace -3 W = span{ 1 1 }. -3…

A: In this question, concept of span is applied. Linear Span Let V represent a vector space, and…

Q: If U is a proper subspace of a finite-dimensional vector space V,show that the dimension of U is…

A: We will prove this by taking help from two theorems. Please see the subsequent steps:

Q: Let U and W be subspaces of V over a ficld F. Show that the union U UW is a subspace if and only if…

A:

Q: Let A be an m×n matrix. Then the null space of A is a subspace of Rn true or false?

A: Given: The statement is "let A be an m×n matrix, then The null space of A is a subspace of Rn".…

Q: Show if W is a subspace of the vector space X, then W is convex.

A: Definition used: A set K in a vector space V is called convex if and only if  x, y belongs to K,…

Q: If A is a normed subspace of E, proof that bd(A) is a subspace of X.

A: Please check the answer in the next step

Q: Determine whether S={a, +a,x+a,x :a, +a, +a, = 0} is a subspace of P.

A: Here S is a subspace of P2

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

A:

Q: The empty subset of any vector space V is not a subspace of V. True False

A: The empty subset of any vector space V is not a subspace of V The given statement is false.

Q: Prove that the set of vectors of the form (a, b, c) where b = a +c is a subspace of R³.

A: According to the given information, it is required to prove that:

Q: Let H and G be subspaces of a vector space V. Show that HnG is a subspace of V.

A: We have to show that intersection of two subspaces is a subspace.

Q: Prove that the set ? = {(a + b, a -b): a and b are real numbers} is a subspace of ℝ2 with the…

A:

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: 1. Show that WW10 W2 is a vector subspace of V, but that W1 U W2 need not be a vector subspace in…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: The set {(x, , x,)' 1 x,+ x, =0} form a subspace of R Select one: O True False

A:

Q: Let W {(a, b, c, d)| a – 5 b = 0 } be a subspace of R*. Then a basis for W is

A: The given subspace of R4 is W={ ( a , b  ,c , d ) | a - 5 b = 0 } Let x=( a, b , c , d ) be in W…

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: Let V be a vector space and let V1, . . . , Vk be a collection of subspaces of V. Prove that V1 ∩ ·…

A:

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

A: Question 1) true  Q. If S and T are subspaces of  a  vector space VTo prove: S∩T is a subspace of…

Q: Theorem 6.14. For any a < b in R, the subspace [a, b] is compact.

A: The objective is to prove that any a≤b in ℝ the subspace a,b is compact. Let's prove the theorem by…

Q: If X is an inner product space, and A is subspace of X, then AL CAO no decision O ACALO A = A++O

A:

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 X = c, the space of all conver gent sequenes and M == (xn) such that , = 0 then M is not…

A:

Q: If y is in a subspace W, then y - ŷ is not zero. Select one: O True O False

A:

Q: Give an example of a vector space V and non-trivial subspaces X.Y. Z of V such thatV =X@Y= X@Z but Y…

A: Give an example of a vector space V and non-trivial subspaces X, Y, Z of V such that…

Q: Show that a subset W of a vector space V is a subspace of V if and only if span[W] = W.

A:

Q: If V is a vector space and W is a subset of V that contains the zero vector then W must be a…

A: Given statement If V is a vector space and W is a subset of V that contains the Zero vector and W…

Q: Let V be the vector space of symmetric 2 × 2 matrices and W be the subspace -4 -3 -3 5 W = span{ |}.…

A:

Q: Show that the set W={(x,y,1)|x and y are real} is not subspace of R3.

A:

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

A: SOLUTION-

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 S and T are subspaces of V, then SNT is a subspace. Select one: O True O False

A: Then 0 or additive identity belongs to S and T  Therefore 0 ∈S∩T so that S∩T =∅ Let x, y ∈ S ∩ T…

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:

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

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

Q: Let V = M22 and W = {invertible 2 x 2 matrices}. Determine whether W is a subspace of M2. %3D

A:

Q: Let Mnn be a vector space of n x n matrices. Which of the following is not a subspace of Mnn?

A: The vector space of nxn matrix is Mnn.

Q: Show that an arbitrary linear combination of two states Vs in the vector space V with the same…

A:

Q: Let A be the vector space of all 2 x 2 matrices over R. Is B a subspace of A? B = {X € A : X² = X}…

A:

Q: 5. Let S = {x + 1,x2 – 2, x – 1,3}. Find a basis for the subspace W that is spanned by S.

A:

Q: If X is an inner product space, and A is subspace of X then A = AL %3D O True O False

A: TRUE

Q: Consider the subspaces U = span{[1 -4 -5],[-1 –6 -13]} and W = span{[4 -4 4],[-2 0 -2]} of V = R'x3.…

A: Any vector belongs to a space spanned by v1 and v2 is the linear combination of v1 and v2.

Q: Determine whether the set W is a subspace of R3 with the standard operations. w = {(x1, 0, x3): X1…

A:

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: If y is not in a subspace W, then y-y is zero. Select one: O True O False

A:

Q: Consider the subspaces U = span{[3 -3 1],[12 3 -7]} and W = span{[-3 2 0],[1 8 -6]} of V = R1x3.…

A:

Q: Show that W={(x1,x2,x3,x4) : x4-x3=x2-x1} is a subspace of R^4  spanned by vectors…

A:

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…

Q: Suppose U and W are subspaces of V for which UUW is a subspace. Show that UCW or W CU.

A:

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.