Exercises 2730 refer to V = C[0, 1], with the inner product given by an integral, as

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Exercises 27–30 refer to V = C[0, 1], with the inner product given by an integral, as in Example 7.

Let V be the space C[-2, 2] with the inner product of Example 7. Find an orthogonal basis for the subspace spanned by the polynomials 1, t, and t².

Data From Example 7

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Linear Algebra And Its Applications

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Authors: David Lay, Steven Lay, Judi McDonald

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Exercises 2730 refer to V = C[0, 1], with the inner product given by an integral, as

Question:

EXAMPLE 7 For f, g in C[a, b], set (J₁8) = ². (f.g) a f(t)g(t) dt Show that (5) defines an inner product on C[a, b]. (5)

Step by Step Answer:

The inner product is g ftgtdt Then 1 and t are orthogonal because 1 1 t dt 0 So ...View the full answer

Linear Algebra And Its Applications

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