Question

In: Math

1,Let v=(1,1)v=(1,1) be a vector in the xy-plane. Find a planar vector w which has length...

1,Let v=(1,1)v=(1,1) be a vector in the xy-plane. Find a planar vector w which has length 2√2, has a positive first component and is perpendicular to v.

W=(,)

2, Find the points where the line l(t)=(1−t,1+t,t) intersects the plane z=x+y

(Give the answer in the form of comma separated list of points like (*,*,*), (*,*,*)

Solutions

Expert Solution

if satisfied with the explanation, please rate it up..


Related Solutions

Questionnnnnnn a. Let V and W be vector spaces and T : V → W a...
Questionnnnnnn a. Let V and W be vector spaces and T : V → W a linear transformation. If {T(v1), . . . T(vn)} is linearly independent in W, show that {v1, . . . vn} is linearly independent in V . b. Define similar matrices c Let A1, A2 and A3 be n × n matrices. Show that if A1 is similar to A2 and A2 is similar to A3, then A1 is similar to A3. d. Show that...
Let V be a vector space and let U and W be subspaces of V ....
Let V be a vector space and let U and W be subspaces of V . Show that the sum U + W = {u + w : u ∈ U and w ∈ W} is a subspace of V .
(10pt) Let V and W be a vector space over R. Show that V × W...
(10pt) Let V and W be a vector space over R. Show that V × W together with (v0,w0)+(v1,w1)=(v0 +v1,w0 +w1) for v0,v1 ∈V, w0,w1 ∈W and λ·(v,w)=(λ·v,λ·w) for λ∈R, v∈V, w∈W is a vector space over R. (5pt)LetV beavectorspaceoverR,λ,μ∈R,andu,v∈V. Provethat (λ+μ)(u+v) = ((λu+λv)+μu)+μv. (In your proof, carefully refer which axioms of a vector space you use for every equality. Use brackets and refer to Axiom 2 if and when you change them.)
1. Let V and W be vector spaces over R. a) Show that if T: V...
1. Let V and W be vector spaces over R. a) Show that if T: V → W and S : V → W are both linear transformations, then the map S + T : V → W given by (S + T)(v) = S(v) + T(v) is also a linear transformation. b) Show that if R: V → W is a linear transformation and λ ∈ R, then the map λR: V → W is given by (λR)(v) =...
Let Vand W be vector spaces over F, and let B( V, W) be the set...
Let Vand W be vector spaces over F, and let B( V, W) be the set of all bilinear forms f: V x W ~ F. Show that B( V, W) is a subspace of the vector space of functions 31'( V x W). Prove that the dual space B( V, W)* satisfies the definition of tensor product, with respect to the bilinear mapping b: V x W -> B( V, W)* defined by b(v, w)(f) =f(v, w), f E...
Let (V, ||·||) be a normed space, and W a dNormV,||·|| -closed vector subspace of V....
Let (V, ||·||) be a normed space, and W a dNormV,||·|| -closed vector subspace of V. (a) Prove that a function |||·||| : V /W → R≥0 can be consistently defined by ∀v ∈ V : |||v + W||| df= inf({||v + w|| : R≥0 | w ∈ W}). (b) Prove that |||·||| is a norm on V /W. (c) Prove that if (V, ||·||) is a Banach space, then so is (V /W, |||·|||)
Find a vector perpendicular to the line 2y=5-3x in the xy-plane.
Find a vector perpendicular to the line 2y=5-3x in the xy-plane.
find the projection vector of the vector v = (2,3,5) onto the plane z = 2x...
find the projection vector of the vector v = (2,3,5) onto the plane z = 2x + 3y -1
1. For a map f : V ?? W between vector spaces V and W to...
1. For a map f : V ?? W between vector spaces V and W to be a linear map it must preserve the structure of V . What must one verify to verify whether or not a map is linear? 2. For a map f : V ?? W between vector spaces to be an isomorphism it must be a linear map and also have two further properties. What are those two properties? As well as giving the names...
Prove the following: Let V and W be vector spaces of equal (finite) dimension, and let...
Prove the following: Let V and W be vector spaces of equal (finite) dimension, and let T: V → W be linear. Then the following are equivalent. (a) T is one-to-one. (b) T is onto. (c) Rank(T) = dim(V).
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT