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b) Let T:R³ →R* be a linear transformation, and let B = {ei, ez, e3} be the standard basis for R³. Suppose that, 3 0 0 3 B [8]. i) Find 7(v), where v= 8 ii) Is w = --- in R(T)? iii) Find the null space of T. T(e) : H T(e2)= T(e3)=

b) Let T:R³ →R* be a linear transformation, and let B = {ei, ez, e3} be the standard basis for R³. Suppose that, 3 0 0 3 B [8]. i) Find 7(v), where v= 8 ii) Is w = --- in R(T)? iii) Find the null space of T. T(e) : H T(e2)= T(e3)=

Elementary Linear Algebra (MindTap Course List)
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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b) Let T:R →R* be a linear transformation, and let B = {ei, e2, e3} be the standard basis for R³. Suppose that, 3 T(e1) T(e2) 3 T(es) i) Find T(v), where v=-1 8 ii) Is w in R(T)? iii) Find the null space of T.
Transcribed Image Text:b) Let T:R →R* be a linear transformation, and let B = {ei, e2, e3} be the standard basis for R³. Suppose that, 3 T(e1) T(e2) 3 T(es) i) Find T(v), where v=-1 8 ii) Is w in R(T)? iii) Find the null space of T.
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