On 10/25/99, taylorwh asks about Q17 of MA322-005,10 Section 3.5 and 3.6 (Oct 26): Can you go over this one in class? Response: Yes. The answer will be the ratio of the number of these 81 matrices whose determinant is not zero to 81. Thanks for asking about this: There was a typo in the key which has now been fixed.

On 10/26/99, claybomi asks about Q16 of MA322-005,10 Section 3.5 and 3.6 (Oct 26): I guessed on this one. I don't understand this. Response: Use the fact that rank(A) = dimension of column space. Since Ax = b doesn't have a solution for some b, that means that the column space is not all of R^3. What does this say about how rank(A) and 3 are related?

On 10/26/99, claybomi asks about Q17 of MA322-005,10 Section 3.5 and 3.6 (Oct 26): could you explain this one in class. Response: See my remark above.

On 10/26/99, claybomi asks about Q18 of MA322-005,10 Section 3.5 and 3.6 (Oct 26): I guessd on this one also. Would you please go over it. Response: Use the fact that if u and x are column vectors then the matrix product of u with the transpose of x is a square matrix whose columns are scalar multiples of u.

On 10/25/99, kendigbr asks about Q15 of MA322-005,10 Section 3.5 and 3.6 (Oct 26): I still don't agree with this could you go over it?? Response: I think we beat this one to death in class. All four dimensions can be calculated immediately upon determining the rank of the matrix A, using the facts that rank(A) = dim(C(A)) = dim(R(A)) and dim(C(A) + dim(N(A)) = #cols of A and dim(R(A))+dim(L(A)) = # rows of A.

On 10/25/99, taylorwh asks about Q17 of MA322-005,10 Section 3.5 and 3.6 (Oct 26): Can you go over this one in class? Response: See my remarks above.