Question

1.

Use Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where

y = y(x)

and

z = z(x).)

−x	+	2y	−	z	=	0
−x	−	y	+	2z	=	0
2x			−	z	=	3

2.Use Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of z, where

x = x(z)

and

y = y(z).)

3x	−	y	+	z	=	4
4x	−	y	+	z	=	2

3.Use Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of z, where

x = x(z)

and

y = y(z).)

4x	−	y	−	z	=	0
x	+	y	+	z	=	5

4.Use Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where

y = y(x)

and

z = z(x).)

2x	−	y	+	z	=	3
−x	+	0.5y	−	0.5z	=	2.5

Answer 1

1)

-x + 2y - z = 0

- x - y + 2z = 0

2x - z = 3

hence, solution is

x = 3 , y = 3 , z = 3

2)

3x - y + z = 4

4x - y + z = 2

x = - 2

y - z = - 10

y = - 10 + z

x = - 2 y = - 10 + z