Assume that T is a linear transformation, T: R3 → · R², T(e,) = ( 1, 3 ), T(e2) = ( 4,– 7 ), and T (e;) = (-5, 4) where e,, e2, ez are the columns of the 3 x 3 identity matrix. Determine if the specified linear transformation is а) one-to-one b) onto

Elementary Linear Algebra (MindTap Course List)
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Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
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Assume that T is a linear transformation,
T: R3 →
· R?, T(e,) = ( 1, 3), T(e2) = ( 4,–7 ), and T (e;) = (-5, 4)
where e,, e2, ez are the columns of the 3 x 3 identity matrix. Determine if the specified linear
transformation is
а)
one-to-one
b)
(Justify each answer)
onto
Transcribed Image Text:Assume that T is a linear transformation, T: R3 → · R?, T(e,) = ( 1, 3), T(e2) = ( 4,–7 ), and T (e;) = (-5, 4) where e,, e2, ez are the columns of the 3 x 3 identity matrix. Determine if the specified linear transformation is а) one-to-one b) (Justify each answer) onto
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