) lat D be a subset of R, ie (De R$ ) and let 5 be a subsel of R$ls C R3) defmedt by D=dczy,2)E R° Z-3oc -2y) nd fle y2)E R = 191=21x+ Si>1), respechaly Z-300 %3D RS -Show that D is a vector subspace of Delemine he bais of D ahd As dimension dincor b Sa vector subipace of R*? Jestily

Q: construct a normal vector normal to the plane containing the indicated points:   P(-5,0,4)…

A: Three points are given. From these three points we can form two lines  PQ and PR These two lie on…

Q: •1/₂ √₁ r(u, v) = 0 ≤u≤ 1,0 ≤ v ≤ T Evaluate 1 + x² + y²dS, where S is the helicoid with vector…

A:

Q: Lee r4)= < Cos (4) t sin (t), sin (2)-t cos (+) }, LOS Compute both the Dormal Vector NCt) to r(t)…

A:

Q: - 15 - 13 -1 Let y = and v2 Find the distance from y to the subspace W of R“ spanned by v, and v2,…

A:

Q: Hhewet Fint projection and Vector projiction ofBonto Afar: A-B, angte between A andBslength_of - -A=…

A:

Q: HConsider the vector space R° (over R) and ZcR consisting of vectors z=(z1, z2 z3), with these…

A: Given Z⊂R3, where R3 vector space.z→=(z1,z2,z3)(a) z1=0(b) z1+z2=0(c) z1+z2=1We have to check in…

Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw() = 4 6 V= 19 16 and -5

A:

Q: The divergence of the vector G = 2i+ sin y j+ 3k is :- -8y + x3 -8y siny + cosy O Option 3 O Option…

A:

Q: O IP R = (i+ ();+(rZ lnt) k is the pusitian vechar of apurticule in spuce defermine at tei W the…

A: Solution:

Q: 2) Let X be a vector space over IR and fa real valued fanctional on Such that (a) pexty) s pix)…

A:

Q: If V and W are subspaces of R", then their union VUW must be a subspace R" as well. True False of

A: given that V and w are the subspaces of a real Vector space. therefore, Since V is a subspace of a…

Q: {{},} Let W be the subspace of R3 spanned by write j = |3 3 as the sum of a vector in W and a vector…

A:

Q: Let the set U = b:c = a = R3 be given. Then which of the following statement or statements are…

A:

Q: Question - s be the subspace ob R spanned by the (x,M»,' and y=Cy, Yo, y,)' Let A = show that = N…

A: We will prove the given statement.

Q: b.) show that IR³ - W₁ + W₂. t C.) Find a subspace V such that IR³ =W₁ U.

A:

Q: Let W be the subspace spanned by the u's. Write y as the sum of a vector in W and a vector…

A:

Q: Q7) Let V is a subspace of R", with an orthognal basis|v1,V2,...,Vp. a) Prove that Proj,v,=v1 b)…

A:

Q: 4 6' Let S be the subspace of R° spanned by the vectors and and let b = 3 Find the point in 4 S that…

A:

Q: 1 for which x value span the vector subspace? -1 13 - 2 -1 O A) 2 в) .1 O C) 0 D) 1 O E) -2

A: We have to find x

Q: Let f(x, y) = ln (1 + x² + y²), then a) f is not differentiable at (0, 0). b) Exists a point (xo,…

A: We are given the function fx, y=ln1+x2+y4. Our aim is to choose the correct option for the given…

Q: 3) Find the dimension of the vectora space ganenated by the yeetons: '= (o 1 82= (2 -1 5 4) 83- (4 0…

A:

Q: V = M2x2 (R) let M = { A€ V A = A²} N = { A = V A = -A ² } Subset of the vector space V V = MON…

A:

Q: YouTrylt 4 Find a vector function r(t) that parameterizes the intersection of the elliptic cyl 9 4…

A:

Q: bläi 3 The direct sum of subspaces U and W of vectors spaces V denoted by إجابتك

A: Representation of direct sum given below.

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: What is the formula for a projection of u onto d where d # 0? Find two different 2 x1 vectors u such…

A: We are only allowed to solve one question at a time and up to three sub-parts. So, we will answer…

Q: What is the dimension of the subspace H of R? spanned by 2 -4 4 32- :? -5 10 -10 O A) 0 O B) 3 O ) 4…

A: The number of vectors in a basis of a vector space is said to be the dimension of that vector space…

Q: let V = M2x2 (R) M = { A € V A = A} N = {AEV A = -A²} Subset of the vector space V The answer must…

A: Direct sum of the subspaces

Q: Find the closest point to y in the subspace W spanned by U₁ and 02. 2 2, U2 23 13) y = 13 9 41 =

A:

Q: Let u= and w- Find the unique vector v in R'such that u.v 1, v is orthogonal to w, l|v|| V3, and y>…

A:

Q: b) The tangent subspace Wp at p ES is the plane through 0 with normal vector p. Find an explicit…

A: b) The tangent subspace at a point p on the unit sphere is the plane through the origin with normal…

Q: and W Consider the subspaces V = {(x. v. Z. w) : 6x = w, y = 3z} ((x, y, z, w): y-4z + 2w = 0} of…

A: