1. Use matrix inversion to solve the given system of linear equations. (You previously solved this system using row reduction in Chapter 2.)

x	+	2y		z	=	0
x		y	+	2z	=	0
2x				z	=	2

(x,y,z) =

2. Use matrix inversion to solve the given system of linear equations. (You previously solved this system using row reduction in Chapter 2.)

2x	+	y	=	2
2x		5y	=	2

(x,y) =

3. Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = x + 2y subject to

x	+	5y		28
3x	+	y		28
x 0, y 0.

c =
x =
y =

4. Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Maximize p = x + 2y subject to

x	+	5y		11
4x	+	y		6
x 0, y 0.

p =
x =
y =

5. Use matrix inversion to solve the collection of systems of linear equations. HINT [See Example 4.]

(a)

x		4y	+	2z	=	4
x	+	2y		z	=	3
x	+	y		z	=	8

(x,y,z) =

(b)

x		4y	+	2z	=	2
x	+	2y		z	=	1
x	+	y		z	=	0

(x,y,z) =

(c)

x		4y	+	2z	=	0
x	+	2y		z	=	0
x	+	y		z	=	0

(x,y,z) =