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College of the Redwoods Mathematics Department Math Math 45 Linear Algebra Quiz 7 Linear Algebra David Arnold c 2000 darnold northcoast com Copyright Last Revision Date October 29 2001 Version 1 00 Directions Place your solution in the space provided No calculators allowed Exercise 1 Consider the independent vectors 1 1 0 1 a1 0 a2 0 and 0 0 1 1 a3 0 1 Use the Gram Schmidt algorithm to nd an orthonormal set of vectors q1 q2 q3 that span the same space as the vectors a1 a2 a3 Solutions to Exercises Exercise 1 Step 1 Let A1 a1 1 0 A1 0 0 Step 2 a2 A1 A1 A1 A1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 A2 a2 Step 3 a3 A1 a3 A2 A1 A2 A1 A1 A2 A2 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 A3 a3 Note that A1 A2 and A3 already have so our orthonormal set is 1 0 q1 q2 q3 0 0 length one what a nice teacher 0 1 0 0 0 0 0 1 Exercise 1


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