Page 402 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Figure Ex-28
The accompanying figure shows a rectangular -coordinate system determined by the unit basis vectors i and j and an
29. -coordinate system determined by unit basis vectors and . Find the -coordinates of the points whose -coordinates
are given.

(a)

(b) (1, 0)

(c) (0, 1)

(d) (a, b)

Figure Ex-29

Prove: Any subspace of a finite-dimensional vector space is finite-dimensional.
30.

The basis that we gave for in Example 6 consisted of noninvertible matrices. Do you think that
31. there is a basis for consisting of invertible matrices? Justify your answer.

32. matrices has dimension _________
(a) The vector space of all diagonal

(b) The vector space of all symmetric matrices has dimension _________

(c) The vector space of all upper triangular matrices has dimension _________