A linear transformation from R3-R4 with the V set of vectors x, where T(x)=0, is V...

A linear transformation from R3-R4 with the V set of vectors x, where T(x)=0, is V a subspace of R3?

Expert Solution

Colby Messinger answered 2 years ago

Let T : R2 → R3 be a linear transformation such that T( e⃗1 ) =...

Let T : R2 → R3 be a linear transformation such that T( e⃗1 ) = (2,3,-5) and T( e⃗2 ) = (-1,0,1). Determine the standard matrix of T. Calculate T( ⃗u ), the image of ⃗u=(4,2) under T. Suppose T(v⃗)=(3,2,2) for a certain v⃗ in R2 .Calculate the image of ⃗w=2⃗u−v⃗ . 4. Find a vector v⃗ inR2 that is mapped to ⃗0 in R3.

Let T: V →W be a linear transformation from V to W. a) show that if...

Let T: V →W be a linear transformation from V to W. a) show that if T is injective and S is a linearly independent set of vectors in V, then T（S） is linearly independent. b) Show that if T is surjective and S spans V,then T（S） spans W. Please do clear handwriting!

Find a matrix representation of transformation T(x)= 2x1w1+x2w2-3x3w3 from R3 to a vector space W, where...

Find a matrix representation of transformation T(x)= 2x1w1+x2w2-3x3w3 from R3 to a vector space W, where w1,w2, and w3 ∈ W. Clearly state how this matrix is representing the transformation.

Consider the linear transformation T which transforms vectors x C) in the y-axis. a) Express the...

Consider the linear transformation T which transforms vectors x C) in the y-axis. a) Express the vector X = T(x), the result of the linear transformation T on x in terms of the components x and y of X. by reflection [10 Marks] b) Find a matrix T such that T(x) = TX, using matrix multiplication. Calculate the matrix product T2 represent? Explain geometrically (or logically) why it should be this. c) T T . What linear transformation does this...

The linear transformation is such that for any v in R2, T(v) = Av. a) Use...

The linear transformation is such that for any v in R2, T(v) = Av. a) Use this relation to find the image of the vectors v1 = [-3,2]T and v2 = [2,3]T. For the following transformations take k = 0.5 first then k = 3, T1(x,y) = (kx,y) T2(x,y) = (x,ky) T3(x,y) = (x+ky,y) T4(x,y) = (x,kx+y) For T5 take theta = (pi/4) and then theta = (pi/2) T5(x,y) = (cos(theta)x - sin(theta)y, sin(theta)x + cos(theta)y) b) Plot v1 and...

let l be the linear transformation from a vector space V where ker(L)=0 if { v1,v2,v3}...

let l be the linear transformation from a vector space V where ker(L)=0 if { v1,v2,v3} are linearly independent vectors on V prove {Lv1,Lv2,Lv3} are linearly independent vectors in V

Find a basis for R4 that contains the vectors X = (1, 2, 0, 3)⊤ and...

Find a basis for R4 that contains the vectors X = (1, 2, 0, 3)⊤ and ⊤ Y =(1,−3,5,10)T.

Consider the linear transformation T : P2 ? P2 given by T(p(x)) = p(0) + p(1)...

Consider the linear transformation T : P2 ? P2 given by T(p(x)) = p(0) + p(1) + p 0 (x) + 3x 2p 00(x). Let B be the basis {1, x, x2} for P2. (a) Find the matrix A for T with respect to the basis B. (b) Find the eigenvalues of A, and a basis for R 3 consisting of eigenvectors of A. (c) Find a basis for P2 consisting of eigenvectors for T.

Bound state in potential. Where V(x)=inf for x<0 V(x)=0 for 0 ≤ x ≤ L V...

Bound state in potential. Where V(x)=inf for x<0 V(x)=0 for 0 ≤ x ≤ L V (x) = U for x > L Write down the Schrödingerequation and solutions (wavesolutions) on general form for the three V(x).

2) Consider the Lorentz transformation that maps (x,t) into (x',t'), where t and x are both...

2) Consider the Lorentz transformation that maps (x,t) into (x',t'), where t and x are both in time units (so x is really x/c) and all speeds are in c units also. a) Show that the inverse of the Lorentz transformation at v is the same as the Lorentz transformation at -v. Why is that required? b) Show that x^2 - t^2 = x'^2 - t'^2, i.e., that x^2 - t^2 is invariant under Lorentz transformation

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