Which of the following sets are subspaces of IR 3? 3 Uj = {(x,y, z) EIR ³ | xyz > 0} U2 = {(x, y, z) E R³ | ¤(y – 2) = 0} U3 = {s(1,0,0) + t(0,0, 1) | s,t e IR} U4 = {(0,0,0), (1,0,0), (0, 1,0), (0,0, 1)} U5 = {(0,0,0)} U6 = {(x, Y, z) E R³ | æ + y – z = 0, 2x + y + z = 0} 3 Enter a list of numbers corresponding to subspaces, separated by semicolons. For example, if only Uj and U, are subspaces, then you would enter 1;2

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

A:

Q: 5. Let U and V be subspaces of R". Then UnV and U + V are defined as follows UnV := {x € R" | x € U…

A:

Q: Let pu: R³ → U be the orthogonal projection onto the subspace U = {(x, y, z) = R³: x-y-z=0}.…

A: Introduction: To find a linear variety S' that projects onto S under the orthogonal projection pu,…

Q: Set V = {(x, y) | x ER, YER}. Define addition of vectors by the rule (x, y) + (x, y) = (y + y',x+x')…

A:

Q: Which of the following can be used to conclude that W = {(x, y, z) = R³ |x-2y+z² = 0} does not form…

A:

Q: 27. Let S be the set of all vectors both of y in R' such that x + y -z = 0 and 2x – 3y + 2z = 0.…

A:

Q: Let U be a vector function of position in R3 with continuous second partial deriva- tives. We write…

A: In this mathematical exposition, we are tasked with demonstrating two important vector identities…

Q: Find the orthogonal projection y of y = -{-----} = նշ W = Span ŷ Ex: 1.23 2 6 onto the subspace

A:

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (v) = - C 12 = 0 2 0

A:

Q: Find a vector-valued function, using the given parameter, to represent the intersection of the…

A:

Q: If U = {(x, y, z) : 3x -y-2z = 0} is a subspace of R, then U = %3D %3D %3D A) {(r, y, z) : r - y+ =…

A: Given  U={(x,y,z): 3x-y-2z=0}is a subspace of R3 To find the value of U⊥

Q: 3. Let S, and S, be two subspaces of R such that s, n s, = ((0,0,0,0,.0)) and dimension(S,) =…

A:

Q: u1 O Given a subset U of R² defined by U = |2u1 = u2 Show that U is U2 a subspace of R3

A:

Q: Suppose U = {(x, x, y, y) = F¹: x, y € F}. Find a subspace W of F4 such that F4 = UW.

A: Our objective is given below:

Q: Let W be the subspace spanned by u₁ and u₂, and write y as the sum of a vector in W and a vector…

A:

Q: 6. Which of the following are subspaces of R° ? (x, y, z all bclong to R) (i) W {(x, y, z): x + y +…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Which of the following choices is not a subspace of vector space R? a. (x,y,z):z=x-y b.…

A:

Q: Which of these vector fields are irrotational? Identify all of those that satisfy this property. A B…

A: The given vector fields, A) u=-x, y, 0B) u=-y, x, 0C) u=-x, z, 0D) u=x, y, z We have to find the…

Q: 3. Let S be the subspace of R' given by S = {(x1, x2, T3, T4) : x1 – 2x2 + 4.x3 – 3x4 = 0} %3D - a.…

A:

Q: Find ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

A:

Q: Find the dimension of the subspace of all vectors in R'whose second and third entries are equal. O…

A: Dimension of subspace is 6. Since dimension of R^7 is 7 and the given subspace has second and third…

Q: 6t Let H be the set of all vectors of the form Find a vector v in R such that H = Span{v}. Why does…

A: Given that H be the set of all vectors of the form 6tt5t. Here, v=615. H=span615 Now, H forms a…

Q: Which of the following sets are subspaces of R°? A. ((x, y, z) | x < y < z} B. ((x, y, z) | 5x – 9y…

A:

Q: Let S € R² | xy ≥ 0 Y where S uses the usual definitions for vector addition and scalar…

A: Given subset of is the following :Obviously Here noted that vector addition rule : and scalar…

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = --B 7 010

A:

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (7) 0 -8 v= 0 0·00 ||

A:

Q: S-t The set W = s,te R} is a subspace of R². %3D s+2t Select one: True False

A: the statement W  is a subspace of R^2 is True.

Q: U = {(z,w) ≤ C² : z²+u²=0}, W={(z,w) ≤ C² : Re(z) = Re(w)} Are subspaces of C²?

A:

Q: Consider the following subspaces U, V, W CR³: U = {(x, y, z): x+y=3z=0} V = {(0, c, 0): e ER} W =…

A:

Q: 3) Find a basis for the subspace of R that consists of the intersection of the planes X-3Y = 5Z and…

A: This is a problem of vector space.

Q: Suppose U = {(x,x+ y, x – y, Y, z) E F° : 1, y, z E F}. Then a subspace W of F such that F = U W is…

A:

Q: Q03. be a basis of V. Let V be an n-dimensional vector space over F, with n ≥ 1. Let B = {v₁,...,…

A: Given : V be an n-dimensional vector space over F, with n≥1 and B = v1, v2, ..., vn be a basis of V.…