Page 272 - DMTH502_LINEAR_ALGEBRA

Linear Algebra

Notes 24.5 Review Questions

n
1. Verify that the standard inner product on F is an inner product.
4
4
2. Consider R with the standard inner product. Let W be the subspace of R consisting of all
vectors which are orthogonal to both = (1, 0, – 1, 1) and = (2, 3, – 1, 2). Find the basis for
W.
3
3. Consider C , with the standard inner product. Find an orthonormal basis for the subspace
spanned by = (1, 0, i) and = (2, 1, 1+ i).
1 2
Answers: Self Assessment

7 2
2. (a) = ,
3 3
1 1
3. (1, 0, 1), (1, 0, 1), (0, 1, 0)
2 2

24.6 Further Readings

Books Kenneth Hoffman and Ray Kunze, Linear Algebra
I N. Herstein, Topics in Algebra

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