Consider vị =[1 v2 = | 1) and v3 = ( 0 ) as vectors in R³. Let T: R3→R³ be a linear operator such that 2 (3) T(v,) = T(v2) = ( 0 ) and T(v3) = [ 5 Show that S = is a basis of R3. а.

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 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...
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Consider vị = (1
v2 = |1) and v3 = | 0 ) as vectors in R3.
Let T: R3→R³ be a linear operator such that
2
T(v,) =
T(v2) = ( 0 ) and T(v3) = ( 5
a. Show that S =
is a basis of R3.
Transcribed Image Text:Consider vị = (1 v2 = |1) and v3 = | 0 ) as vectors in R3. Let T: R3→R³ be a linear operator such that 2 T(v,) = T(v2) = ( 0 ) and T(v3) = ( 5 a. Show that S = is a basis of R3.
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