Required reading: Section 4.1, 4.2 . We've spend one lecture on `dual spaces'; you may want to review my notes on this (posted on Blackboard under course materials).

Assignment #9 is due on Friday , December 2.

Additional homework (do not hand in).

• Section 4.1, problems 1, 3, 8, 9,
• (1) Prove that if $A,B\in M_{m\times n}(F)$ are in reduced row echelon form, and with $N(L_A)=N(L_B)$, then $A=B$.
• (2) Prove that the reduced row echelon form of a matrix is uniquely determined by the matrix, and does not depend on the order of the row operations used. Hint: Use (1) above.