Help with Discrete Math Problems
- To: mathgroup@smc.vnet.net
- Subject: [mg11230] Help with Discrete Math Problems
- From: lquinn@mindspring.com
- Date: Mon, 2 Mar 1998 23:11:17 -0500
- Organization: MindSpring Enterprises, Inc.
Can someone please help me solve this problems. Thanks
Consider the following system of eq. Use expansion by cofactors to
obtain the simultaneous solution
1 1 1 : -2
3 3 -1 : 6
1 -1 1 : -1
b) Obtain the inverse using Expansion by Cofactors
c) Give the solution vector
Use the Gram-Schmidt algorithm to orthoganalize the x matrix sometimes
called the design metrix then obtain the solution. Comment on the form
X' X" . Does this form offer any computational advantages. e.g. in
terms of the number of steps, number of calculations.
Y = Xb
Y X b
11 1 -4 1 3
12 1 3 2 -5 b0 10
1 1 3 -4 b1 12 1
4 4 -8 b2 11 1 -3
5 -2 b3 14 1 -1 6
-5
Consider U below. Show that the vectors in U are Orthogonal
U
1 -3 5 -1
1 -2 0 1
1 -1 -3 1
1 0 -4 0
1 1 -3 -1
1 2 0 -1
1 3 5 1
Comment on finding the inverse of U' U
Now suppose that Y is specified as
Y: (5.8, 3.1, 3.2, 6.0, 7.3, 8.1, 6.2) and U is the problem above
What is the @0, @1, @2, @3, in the matrix @x read as Alpha sub zero,
alpha sub one, alpha sub two, etc.
U' Y = U' U@
Write out the four equations in algebraic form.