b) Let T:R³ R³ be a linear transformation, and let B = {e1, e2, e3} be the standard basisfor R³.Suppose that,T(e₁) =ГОT(e₂) = 3LoT(e3) = 0-i) Find T(v), where v= 2[5]ii) Is w6 in R(T)?c) Define the linear transformation T: R³ →R² bya-3cT([]) = [a²4-7²³²]+bFind a basis for the null space of T and its dimensionV7-31471030

b) Let T:R³ R³ be a linear transformation, and let B = {e1, e2, e3} be the standard basis for R³. Suppose that, T(e₁)=1 -1. T(e₂)=3 T(e3)=0 i) Find T(v), where v= 2 ii) Is w=6 in R(7)? -191 c) Define the linear transformation T: R³ →R² by a - 3c T([*]) = [47³] +b- Find a basis for the null space of T and its dimension

b) Let T:R³ R³ be a linear transformation, and let B = {e1, e2, e3} be the standard basis for R³. Suppose that, T(e₁)=1 -1. T(e₂)=3 T(e3)=0 i) Find T(v), where v= 2 ii) Is w=6 in R(7)? -191 c) Define the linear transformation T: R³ →R² by a - 3c T([*]) = [47³] +b- Find a basis for the null space of T and its dimension

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 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...

See similar textbooks