: 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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