On 10/19/99, nged asks about Q10 of MA322-005,09 Section 3.3 and 3.4 (Oct 21): can u show me how to solve this questions, cause i just guess it. Response: One way to reason this is as follows. Since the rank is 3 there are 3 pivot variables, so that means we can solve the 3 equations for 3 of the variables in terms of the other 2 (which will be the free variables). Hence there will infinitely many solutions to the matrix equation. Note that if the rank had been less than 3, say 2, then we could solve 2 equations for two variables in terms of the other 3 and the 3rd equation would reduce to something of the form 0 = b. So the matrix equation would have 0 or infinitly many solutions depending on whether b is not 0 or 0.

On 10/21/99, downeyad asks about Q2 of MA322-005,09 Section 3.3 and 3.4 (Oct 21): in section 3.2, on an example problem, it tells us to set a free variable equal to one, the other free variables to zero, then solve for the pivot variables. The answer to this homework question is the exact opposite. Which is correct? Response: Ouch! The key has a typo. I have fixed it. Thanks for finding it.