Page 493 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 493
(a) (1, 1, 1, 1)
(b)
(c)
In each part, an orthonormal basis relative to the Euclidean inner product is given. Use Theorem 6.3.1 to find the
11. coordinate vector of w with respect to that basis.
(a) ,
;
(b) ; , ,
12. Let have the Euclidean inner product, and let be the orthonormal basis with ,
.
(a) Find the vectors u and v that have coordinate vectors and .
(b) Compute , , and by applying Theorem 6.3.2 to the coordinate vectors and ; then check
the results by performing the computations directly on u and v.
13. Let have the Euclidean inner product, and let be the orthonormal basis with ,
, and .
(a) Find the vectors u, v, and w that have the coordinate vectors , , and
.
(b) Compute , , and by applying Theorem 6.3.2 to the coordinate vectors , , and ;
then check the results by performing the computations directly on u, v, and w.
