1) Let T a b la + 2b +2c + 1d + 7e+ (-1) f la + 2b + 4c + 4d +21e+(-2)ƒ la + 2b +3c+ 2d + 12e + (-2) f la + 2b + 1c + (-1) d + (-2) e +0f] Then an orthogonal basis for Ker(T) would be: Note that if you do not need a basis vector, then write 0 for all entries of that basis vector. For example, if you only need 2 vectors in your basis, then write 0 in all boxes corresponding to the third vector
1) Let T a b la + 2b +2c + 1d + 7e+ (-1) f la + 2b + 4c + 4d +21e+(-2)ƒ la + 2b +3c+ 2d + 12e + (-2) f la + 2b + 1c + (-1) d + (-2) e +0f] Then an orthogonal basis for Ker(T) would be: Note that if you do not need a basis vector, then write 0 for all entries of that basis vector. For example, if you only need 2 vectors in your basis, then write 0 in all boxes corresponding to the third vector
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 10EQ: In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem...
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