HW #7, due 3:50pm Friday, March 30

4.4 Coordinate systems

2.

36.

4.5 Dimension

12. (Dimension of subspace of R3 spanned by 4 vectors.)

14. (Dimensions of Nul A and Col A.)

16. (Dimensions of Nul A and Col A.)

19. (True or False, and why)

20. (True or False, and why)

4.6 Rank

2. (Bases for Col A, Row A, Nul A given RE form.) Note that the non-zero rows of a row-echelon form of A form a basis for Row A.

18. (True or False, and why)

22. (10 equations in 12 unknowns.)

X. (a) Construct a random integer-valued 5x9 matrix A of rank 3. (b) Compute a row-echelon form of your matrix and say how it verifies that the rank of A is 3.

4.7 Change of basis

2.

8.