Math 54 quiz 5 let a be an m times n matrix which of the

Question

MATH 54 QUIZ 5-

1. Let S be a subset of an n-dimensional vector space V, and suppose S contains fewer than n vectors. Explain why S cannot span V.

2. Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A. Then find bases for Col A, Row A, and Nul A.

3. If A is a 7 × 5 matrix, what is the smallest possible dimension of Nul A?

4. Let A be an m × n matrix. Which of the subspaces Row A, Col A, Nul A, Row A^T, Col A^T, Nul A^T are in R^m and which are in Rⁿ? How many distinct subspaces are in this list?

5. Let

be bases for R². Find the change of coordinate's matrix from B to C and the change of coordinate's matrix from C to B.

6. Show that {ln 2, ln 3, ln 5} is linearly independent when R is considered as a vector space with scalars in Q.

7. Write anything you like here (comments, questions, suggestions, etc).