Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R b)show that R° = F1 + F4

Q: Prove thatII = {(x, y, z)|x – 2y+ 3z = 0}is a subspace of JR³, %3D -

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

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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: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

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: Let W = {a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to O…

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Q: _. Let u = 6 " and let W be the set of all x in R3 such that u x = 0. (a) Show that W is a subspace…

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Q: Let H = Span{₁,..., If u € R¹ satisfies vú = v½ u then u belongs to H¹. p} be a subspace of R" . =…

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Q: Let V = {(x, y, 2x – 3y)|x, yɛR}. Prove that V is closed for addition and scalar multiplication i.e.…

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Q: Let W = {a + bx + cx + dx| a+ b = 0 and c – 3d = 0} be a subspace of P3 Then the dimension of W is…

A: Linear combination of vectors we use to find.

Q: Let V be the set of vectors (x, y, z) E R° such that r(y² + z2) = 0. Is V a subspace of R³?

A: 16. Let V be the set of vectors x, y, z∈ℝ3 such that  xy2+z2=0 We have to check whether V is a…

Q: Let V = {ax* + bx² + c : a, b, c E R}. Is V a subspace of P4?

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Q: Let H be the set of all vectors given by   Find vectors u and v in R^3 such that H = span{u, v}.…

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Q: :) Let T : U = р — 2q — 0, р, 9, r, s E R Is U a subspace of M2.2(R), if so, find its basis and…

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Q: The vector x is in a subspace H with a basis B= {b, ,b2}. Find the B-coordinate vector of x. x= [x]B

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Q: Let S be the subspace of Rn spanned by the vectors x1, x2, . . . , xk. Show that y ∈ S⊥ if and only…

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Q: to the subspace W = Span{u1, u2} where 0. Find the distance from the vector y and u2 = -2 O 2 01

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Q: What is the dimension of the subspace W = {A = [aij] € R4x5|a45 = 0} dimW = Ex: 5

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Q: 2. Show that U = {(x,y, x) : , y E R} is a subspace of R$. Then, find a linear complement of U in R.…

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

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Q: Let S consists of all vectors of the form (x, 0, y, 0) in R* whe y are real numbers. Determine…

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Q: .a. Is the set of vectors W = {(x,y,z) x,y,z € R,x=z+2} subspace of R³?

A: Given that a) W=x,y,z|x,y,z∈ℝ,x=z+2 of ℝ3. b) W=pt-tq of M22 Check the space W is the subspace of…

Q: Consider the set S = {(x, y, z) ∈ R3 | x - 2y = z}. (a) Show that S contains the zero vector. (b) Is…

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Q: Find the orthogonal projection of V = nto the subspace W of R* spanned by Uj = U2 = Uz = -6/4 -6/4 w…

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Q: Find a basis and dimension of the subspace described as follows:{(x, y, z, w) |2x + 5y – z=0} (0-0)…

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Q: What is the dimension of w = {A € M2x2 (R) : A"| =ö} ĄT -2 1 2 This is not a subspace

A: W=AEM2×2(R) : AT1-2=→0  Let A=abcd, a,b,c,dER     AT=acbd     AT1-2=→0  ⇒acbd 1-2 =00 ⇒a-2cb-2d=00…

Q: Find the closest point to y in the subspace W spanned by vị and vz 2 y =| 1 ,v1 0,v2 -2 2 а) b) c)…

A: The following is the solved answer.

Q: Let S be the collection of vectors [] in R² that satisfy the given property. In each case, either…

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

Q: Let W = (a + bx + cx2 + dx'| c- 3d = 0} be a subspace of P. Then the dimension of W is equal to O…

A: dim(W) = number of vector in the basis of W.

Q: ind the closest point to y in the subspace W spanned by vị and v2 2 y =| 1 |,v1 = ,V2 = |-2 2 а) b)…

A: We will use the following method.

Q: Is M = {(x,y,z)|x is nonnegative} a subspace of R³? Yes or No? Justify or give/find a…

A: Given  M =  x, y, z  x is nonnegative

Q: Suppose U = {(x, y,x + y,x – y, 2x) e F° : x, y e F}. Find a subspace W of F such that F5 = U + W.

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Q: Is W = ((x,y) | xy=0} a subspace of R??

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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. ,

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Q: Q. Show that (a,b,c) where c=a+b is subspace of R

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Q: Let W = {(x, y, 1) | x, y, E R}. Is W a subspace of R3?

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Q: 4) Find all values of h such that Y will be in the subspace of 3. R spanned by VI) V2, V3 if V I V2…

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Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R3 b)show that R' =…

A: Solution of the problem as follows

Q: . Let W be the subspace of R3 spanned by the vectors vj=(1,0,7), v2=(6,1,7), and V3=(14,-1,13). Find…

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Q: Consider the set ? = ((x, x+ y, 2y)|x,y are real) of vectors in r3 . Is W a subspace? If yes, prove…

A: We have Set S = {(x, x + y, 2y) | x, y are real}. Let u, v be any two element of S then,

Q: а о if v = M22 ( R) and W = { : а , bE R } 0 a then .a W is not subspace of .b W is subspace of

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Q: Let W be the set of all vectors of the form b. 3c - 2 b C where b and ceR. Find vectors u and v such…

A: Spanning set

Q: Let W = { |xy <0}. Is W a subspace of R?? If so, use generic terms to demonstrate the necessary…

A: W is not a subspace of R2.

Q: Is Y = (x,y,z) | y=z} a subspace of R?

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Q: Find the orthogonal projection of V = onto the subspace W of R' spanned by U1 = , U2 Uz = VW ||

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Q: Let U and W be subspaces of R³ for which dimU=1, dimW=2, and UgW. Show that R=UOW.

A: I have shown all the conditions of direct sum of two subspaces

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

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Q: Show that U = {(r, y, z): r.ye R} is a subspace of R³. Then, find a linear complemen

A: Here a subset of ℝ3 is given as U=x, y, x: x,y∈ℝ

Q: Explain why S = {(r,y) : x, y € R, x > 0} is not a subspace of R²

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Q: Find the closest point to y in the subspace W spanned by vị and vz 2 1 y =| 1 |,v1 =| 0 [0] 2 lo] 2…

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