Q33 please with explanations (linear algebra question) Problem II Consider a linear transformation L₁ R¹ R³ given below and a linearoperator L₂ R³ R³ given by L₂(x, y, z) = (x + 2y3z, 2x + 5y + z, 3x + 8y + 5z). LetL = L₂0 L₁ be their composition, i.e., L(v) = L₂(L1(v)) for all v € R¹.(i) Find the matrix of the linear transformation L.(ii) Find a basis for the range of L.(iii) Find a basis for the kernel of L.21. L1 (U1, U2, U3, U4) = (v₁ +202, V4, Us).22. L₁(U1, U2, U3, U4) = (U3, 202 - V4, U₁).23. L₁(U1, U2, U3, U4) = (v2 - 2V3, U4, V₁).24. L1 (U1, U2, U3, U4)= (v2V3, V1, 204).25. L1 (U1, U2, U3, U4) = (V4, U₁+U2, U3).26. L1(U1, U2, U3, U4) = (v₁ +2U3, U4, U2).27. L1 (U1, U2, U3, U4) = (303-204, U2, U₁).28. L₁(U1, U2, U3, U4) = (V4, V₁ + V3, U₂).29. L₁(U₁, U2, U3, U4)= (V3-2V4, V₁, V₂).30. L1 (v1, U2, U3, U4) = (v₁ + V₁, V₂ + V₁, Vs).31. L₁(v1, U2, U3, U4) = (v₁, 202 + V₁, V3).32. L₁(v1, U2, U3, U4) = (U3, 202, V1 - V₁).33. L₁(v1, U2, U3, U4)= (V2, V4, V1 - 203).34. L₁(v1, U2, U3, U4) (V2, V1-V3, 204).35. L₁(v1, U2, U3, U4) = (V₁, V2, V₁ + V3).36. L₁(v₁, U2, U3, U4) (203, U4, U1+U₂).37. L₁(v1, U2, U3, U4) (303, 02204, ₁).38. L₁(v1, U2, U3, U4) = (V4, V3, V₁ + V₂).39. L₁(V₁, V2, V3, V₁) (U3, V₁, V₂ - 20₁).-40. L₁(v1, 02, 03, V4) = (V₁ - V₁, V2, V3).==

Given: Lv=L2L1v L1v1, v2, v3, v4=v2, v4, v1-2v3L2x, y, z=x+2y-3z, 2x+5y+z, 3x+8y+5z To find: (i) The…

: Problem II Consider a linear transformation L₁ R4 R³ given below and a linear operator L₂ R³ R³ given by L2(x, y, z) = (x+2y3z, 2x + 5y + 2, 3x + 8y + 5z). Let LL₂0 L₁ be their composition, i.e., L(v) L₂(L₁(v)) for all v R¹. - (i) Find the matrix of the linear transformation L. (ii) Find a basis for the range of L. (iii) Find a basis for the kernel of L. 21. Li (U1, U2, U3, U4)= (1 +202, U4, Us). 22. Li (U1, U2, U3, U4) (Us, 202 U4, U₁). 23. L₁ (U1, U2, U3, U4)= (2-203, U4, U₁). 31. L₁(1, U2, U3, U4) = (v₁, 202 + V4, Vs). 32. Li (U1, U2, U3, U4) = (U3, 202, U₁-V₁). 33. L1 (1, 2, 3, 4) (U2, V4, U1-203). =

: Problem II Consider a linear transformation L₁ R4 R³ given below and a linear operator L₂ R³ R³ given by L2(x, y, z) = (x+2y3z, 2x + 5y + 2, 3x + 8y + 5z). Let LL₂0 L₁ be their composition, i.e., L(v) L₂(L₁(v)) for all v R¹. - (i) Find the matrix of the linear transformation L. (ii) Find a basis for the range of L. (iii) Find a basis for the kernel of L. 21. Li (U1, U2, U3, U4)= (1 +202, U4, Us). 22. Li (U1, U2, U3, U4) (Us, 202 U4, U₁). 23. L₁ (U1, U2, U3, U4)= (2-203, U4, U₁). 31. L₁(1, U2, U3, U4) = (v₁, 202 + V4, Vs). 32. Li (U1, U2, U3, U4) = (U3, 202, U₁-V₁). 33. L1 (1, 2, 3, 4) (U2, V4, U1-203). =

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...

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