MA-305 Homework 4

Due at 4:05pm, Tuesday, October 7, 1997

You may do the calculations necessary for these problems either by hand or with Maple. Please submit a handwritten solution, or email an ASCII/Postscript/html document to the TA. (You may also submit through email which attached your Maple worksheet.)

1. *Show that det(A) = (b-a)(c-a)(b-c) if A is the following.

   	[	a2	a	1	]
   A =	[	b2	b	1	]
   	[	c2	c	1	]

   This determinant is call a Vandermonde determinant.

2. 		[	1	-1	2	]
   *If	A =	[	3	4	1	]	, verify that det(A) = det(AT).
   		[	2	5	1	]

3. *Verify that det(AB) = det(A)det(B) for the following:

   	[	1	-2	3	]			[	1	0	2	]
   A =	[	-2	3	1	]	,	B =	[	3	-2	5	]
   	[	0	1	0	]			[	2	1	3	]

4. *Is det(AB) = det(BA)? Justify your answer.

*: problem from ``Introductory Linear Algebra with Applications'' by Kolman and Hill