Page 495 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

21. The subspace of spanned by the vectors and is a plane passing through the origin.

Express in the form , where lies in the plane and is perpendicular to the plane.

Repeat Exercise 21 with and .
22.

Let have the Euclidean inner product. Express in the form , where is in the space
, and is orthogonal to W.
23. W spanned by and

Find the -decomposition of the matrix, where possible.
24.

(a)

(b)

(c)

(d)

(e)

(f)

Let be an orthonormal basis for an inner product space V. Show that if w is a vector in V, then
25. .

Let be an orthonormal basis for an inner product space V. Show that if w is a vector in V, then
26. .

In Step 3 of the proof of Theorem 6.3.6, it was stated that “the linear independence of ensures that
27. .” Prove this statement.