Prove that if U and V are subspaces of R" and U

Q: 3. Show that the set W = {(x, 0) : x e R} is a subspace of R?.

A: In order to show W is a subspace of R2 , we need to prove W is closed under addition. For any two…

Q: Show that V is a subspace of R³: V is the set of all (x, y, z) such that z = 2x + 3y

A:

Q: Prove that a subset W of a vector space V is a subspace of V if and only if W = ∅, and, whenever a ∈…

A: We need to prove that a subset W of a vector space V is a subspace of V if and only if W = ∅, and,…

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 = {(x1, x2): x1 ≥ 0 and x2 ≥ 0}, with the standard operations, is not a subspace of R2.

A:

Q: Let V = M2x2. W. (R) = € V : a, b, cER W2(R) € V : a € R then prove that W, and W2 are subspaces of…

A: Necessary condition to be a subspace is: Vector addition property Scalar multiplication property.…

Q: Show that W is a subspace of R¹.

A:

Q: Determine if the set W of vectors (x1 , x2) in R such that xr? + x2 = 1 is a subspace of R’.

A: W is not a subspace of R²

Q: 2. Let U and W be subspaces of a vector space V such that UUW is a subspace of V. Prove that UCW or…

A: Given that U and W are subspaces of a vector space V such that union of U and W is a subspace of V.…

Q: 2. Determine whether the set W = {(x,y, z)|x + y +z = 0} is a subspace of R3

A:

Q: Suppose U1,U;, -..Um are finite-dimensional subspaces of V. Prove that U + Uz + .. +Um is…

A: Suppose U1, U2, ... , Um are finite-dimensional subspaces of V. To prove U1+U2+ ... +Um is finite…

Q: 6. Let U and W be 3-dimensional subspaces of a 4-dimensional vector space V, and suppose that U + W.…

A:

Q: True or False: If U and W are subspaces of a finite dimensional vector space and UnW = {0}, then U°…

A:

Q: Let V be a finite-dimensional vector space, and let U, W be subspaces of V. Prove that (U + W)° C…

A:

Q: Prove that W1 = {(a,b) E R² : 4a – b= 0} is a subspace of R2.

A:

Q: 6. Let U and W be 3-dimensional subspaces of a 4-dimensional vector space V, and suppose that U # W.…

A:

Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R. %3D

A: To Prove U is a subspace of vector space V 1) 0∈U  If x, y∈U  and a∈V  2) Closed under vector…

Q: show that if w is a subspace of a finite - dimensional vector space V and dim (w)= dim (V) then W =…

A: In this question, we will use the fact that If dim(W) = dim(V ) = n, then a basis for W is a…

Q: Let U and W denote subspaces of Rn, and assume that U ⊆ W. If dim U = n − 1, show that either W = Rn…

A:

Q: Prove that if S ⊆ R is a vector subspace of R, then either S = {0} or S = R.

A: Here, if s={0} then we are done.  But suppose that S⊂ℝ and S≠{0} is a vector subspace of ℝ to prove…

Q: Suppose V is finite-dimensional and U is a subspace of V such that dim U = dim V. Prove that U = V.…

A:

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 that X = ER' :z + y + z = 0 and ² + y² = z² Determine (with justification) whether X is a…

A: Given  X=xyz∈ℝ3:x+y+z=0 and x2+y2=z2

Q: is

A:

Q: If W is a subspace of R and v is any vector in R", then ||projwv|+|v-projwv||2= |v||2.

A: Introduction: Every vector that doesn't lie in a subspace can be uniquely expressed as a sum of two…

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: 2. Determine if the set S consisting of vectors of the form b where abc = 0 is a subspace of R³.…

A: No, S is not  a subsapce of ℝ3. Explanation: Here,  s1=110 and s2=001 belong to set S. Then,…

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

A:

Q: 2) Let W1, W2 be subspaces of V. Prove that W1 UW2 is a subspace if and only if W1 C W2 or W2 C W1.

A: Let W1,W2 be subspaces of V. To prove W1∪W2 is a subspace if and only if W1⊆W2 or W2⊆W1

Q: 2. Prove that the set S is a subspace of the vector space V.(5 V = R3x3 and S is the set of upper…

A:

Q: Give a counter example to show that W is not subspace of R³. W=set of (x, y, z) where x + y = 1

A:

Q: Show that W = {(a, 0, b)la, b = R} is a subspace of R³.

A: As per guidelines we are supposed to solve the maximum first questions only .kindly post another…

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

A:

Q: Give a counter example to show that W is not subspace of R³. W=set of (x, y, z) where x + y = 1 6. ,

A:

Q: II. Decide which of the following are subspaces of corresponding vector spaces: C R?

A: Vector space.

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 H be the set of all vectors of the form 3s . Find a vector v in R3 such that H = Span {v}. Why…

A:

Q: snip

A: We can represent the given set again as: W=xyz:x=3y+1 and z=-2y Let  w1=x1y1z1∈WThen,x1=3y1+1 and…

Q: 9

A:

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: 5. Let W be a subspace of the vector space V. Prove that the zero vector in V is also the zero…

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: ) Do there exist subspaces S,T, and U of R³ such that S 1 T, SI U, and TiU? if so, provide an…

A: I have considered te subspace generated by orthogonal basis vector.

Q: Let W be an (n – 1)-dimensional subspace of V. Show that V has a basis B satisfying BnW = Ø. |

A: This question is related to vector space . Solution of this question is

Q: Let V = R and W = {x|x = (x1, x2, 1)}, Is W a subspace of V?

A:

Q: Investigate the dimension of the following subspace of R*. All vectors of the form (a,b,c,d), where…

A:

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

A:

Q: i) Let V = M2x2(R) and %3D W; = {(: :) ev:a.hceR} and W2 = {(". :) ev :a,be R Prove that W1 and W2…

A:

Q: let W={(x,,x,,1):x,,x, are real numbers} is W a subspace of R

A: False