Page 457 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 457
(a) Find for , , .
(b) Find if and .
Sketch the unit circle in using the given inner product.
18.
(a)
(b)
Find a weighted Euclidean inner product on for which the unit circle is the ellipse shown in the accompanying figure.
19.
Figure Ex-19
Show that the following identity holds for vectors in any inner product space.
20.
Show that the following identity holds for vectors in any inner product space.
21.
22. Let and . Show that is not an inner product on .
Let and be polynomials in . Show that
23.
is an inner product on . Is this an inner product on ? Explain.
Prove: If is the Euclidean inner product on , and if A is an matrix, then
24.
Hint Use the fact that .
