Q: Determine whether W is a subspace of V.V=F,W= {f in F :f(0) = 0}
A: Here given V be a vector space of function over a field. and W= {f in F :f(0) = 0}
Q: Show that V is not a subspace of R°: V is the set of all (x, y, z) such that x + y +z = 3
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Q: Let V=R²³ be a vector space over R and w = {{ x, y, z) € R³ : x = y +z, y, z, XER} show that w is a…
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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: 3. Let W = {(x,y,z): x? + y? = z}. Is W a subspace of V = R3? %3D
A: We need to check if W is a subspace or not.
Q: Let W = {a + bx + cx? + dx³| a + b = 0 and c – 3d = 0} be a subspace of P3. Then the dimension of W…
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Q: (c) Find a subspace U such that R³ = W₁ OU.
A: C. Hint: Use the result of part (b) in the part (c) and obtain the required result.
Q: Let A = { | 2.x |x € R}. Is A a subspace of R³? З Let B x + y + z = 0}. Is B a subspace of R³?
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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 H be the set of all points in the second and fourth quadrants in the plane V=R^2. That is, H={…
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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: "The set U = {(x, y, z, w) E R* | ¤ – y = z + 2w and r + y – z = w + 1} is a subspace." %3D
A: U=x,y,z,w∈ℝ4|x-y=z+2w and x+y-z=w+1 To find: U is a subspace or not Take x,y,z,w=0,0,0,0 Then,…
Q: et X = {(x,y, z): Vx² + y² + z² <1} be a subspace R° with the standard topology and 0 = (0,0,0).…
A: Given, X=x, y, z:x2+y2+z2 ≤1 be a subspace of R3 with the standard topology and o=0,…
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: Show that S = {(x, Y, z)|4x – y + 5z = 0, x, y, z E R} is a subspace of R³.
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Q: Suppose U = {(z, 2, ,9) *:1,y € F}. Find a subspace W of F such that F* = U e W.
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Q: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y? + z²) = 0. Is V a subspace of R?
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Q: Let H be the set of all points in the third quadrant in the plane V = R². That is, H = {(x, y) | x <…
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Q: Let H be the set of all points in the second quadrant in the plane V=R^2. That is,…
A: Let H be the set of all points in the second quadrant in the plane V=R^2. That is,…
Q: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y?+ z²) = 0. Is V a subspace of R³?
A: Test for subspace for V to be a subspace If u and v are elements of v then u +av must be in V where…
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: Let W = (a + bx+ cx + dx'|a+ b= 0 and c -3d = 0 ) be a subspace of P Then the dimension of W is…
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Q: Which of the following sets is not a vector subspace of p? OA. W = ((x,y)x = 2y} O B. W - ((x,y)y-…
A: Subspace of a vector space
Q: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y²+ z²) = 0. Is V a subspace of R³?
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Q: Let W fa + bx + cx2 + dx'| a+ b 0 and c-3d 0 } be a subspace of Pg. %3D %3D %3D Then the dimension…
A: a+b=0 and c-3d=0 b=-a and c=3d Equation given is; a+ bx+ cx2+ dx3 = a- ax+ 3dx2+ dx3 that can be…
Q: Determine whether U = {(1, s, t)ls,t e R} is a subspace of R.
A: FOR ANY SUBSET U TO BE A SUBSPACE OF ANY VECTOR SPACE V IT IS NECESSARY THAT U HAS ZERO VECTOR IN…
Q: Is T = {(x,y,z)| x+2 y+3z=0} a subspace of R?
A: Subspace
Q: Let W = {a + bx + cx? + dx³|c – 3d = 0} be a subspace of P3. Then the dimension of W is equal to…
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Q: Determine the following is the subspace in R’? W ={(x,y,z):x+y+z=0}
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Q: Let W = {(0, x, y, z): x - 6y + 9z = 0} be a subspace of R. Then a basis for W is: %3D
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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
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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: 3) Explain why S, = {(x, y) E R²:y > 0} and S1 = {(x, x²): x E R} are not subspaces of R?. %3D
A: We will solve both these parts using only basic knowledge of subspaces and vector spaces (in clear…
Q: Is W = ((x,y) | xy=0} a subspace of R??
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Q: 16. Let V be the set of vectors (x,y, z) E R³ such that r(y² +z²) = 0. Is V a subspace of R³?
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Q: Let V = {(x,y) | x,y ϵ R} – the set of ordered pairs in R² . Let W = {(x,0) | x ϵ R} Prove that W…
A: The objective is to prove that W is a subspace of V.
Q: 3) Let W = { (x, y, z, t) : x = 0, y = -z } be subset of IR*. Is W a subspace of IR* ?
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Q: 12. Let K C R" and let V = {x € R" : x ly Vy E K}. Prove that V is a subspace of R".
A: " As per the company guidelines we are supposed to solve first question only. Kindly post the other…
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: - Let V = R and W = {(a, b, c) E V \a + b = c}. Is W a subspace of V? If so, what is its dimension?
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Q: Consider the set S = yl E R : 4x +6z=7y, x – 13y=0 . Is this a subspace of R ? Explain why or why…
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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: Let S be the set of all elements of the form (x + 2y , y , -x + 3y) in R3 , where x,y belongs to R…
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Q: Determine whether the set S is a subspace of R³ or not = {(r, y, z) E R³ : x + 2y – z = 0, 2.x – y +…
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Q: Is Q = {(x,y,z) | x=2y & z=1} a subspace of R?
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Q: Let W = (a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of Py. Then the dimension of W is equal to
A: Here we will find out dimension of W.
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
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- Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,
- Consider the vector spaces P0,P1,P2,...,Pn where Pk is the set of all polynomials of degree less than or equal to k, with standard operations. Show that if jk, then Pj is the subspace of Pk.Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn,WAinMnn:detA=1