MATHEMATICS 201-105-RE
Linear Algebra
Martin Huard
Winter 2005

Assignment #2
Maple Solutions

>	with(linalg):

Warning, the protected names norm and trace have been redefined and unprotected

Question 4

>	A:=<<2 | 5 | -1>, <3 | 4 | 7>, <-5 | 0 | 3>>;

>	B:=<<1 | 2 | 3>, <2 | -3 | 4>, <3 | 4 | -5>>;

>	C:=<<-2 | 2 | 3>, <1 | 3 | 0>>;

(a)

>	evalm( (A+B)^2 );

(b)

>	evalm( A^2+2*A&*B+B^2 );

(c)

>	transpose(C&*inverse(B)&*A);

(d)

>	det(C&*transpose(C));

(e)

>	trace(adjoint(A));

Question 5

(a)

>	Aug:=matrix([[1,2,3,4],[5,6,7,8],[3,5,0,-1]]);

>	backsub(gaussjord(Aug));

Hence the solution is ( ).

(b)

>	Augb:=matrix([[1,2,0,3,-1,2],[3,6,5,1,0,1],[-3,-6,-10,7,-3,4]]);

>	backsub(gaussjord(Augb));

Hence the solution is ( ).

Question 7

(b)

>	P:=matrix([[0.85,0.10,0.15],[0.1,0.85,0.05],[0.05,0.05,0.80]]);

>	X0:=<<0.5>, <0.4>, <0.1>>;

>	X4:=evalm(P^4&*X0);

Hence the share of audience that each network will command after 4 weeks is 45.1% for CTV, 38.1% for CBC and 16.8% for Global.

>	X52:=evalm(P^52&*X0);

Hence the share of audience that each network will command after 1 year is 44.0% for CTV, 36.0% for CBC and 20.0% for Global.