If it is dependent, find the complete solution. (If the system is dependent, express your answer in terms of t, where x = x(t),

Question

Determine whether the system of linear equations is inconsistent or dependent.

	x	+	y	+	z	=	4
y	−	3z	=	11
2x	+	y	+	5z	=	−5

dependentinconsistent    

If it is dependent, find the complete solution. (If the system is dependent, express your answer in terms of t, where x = x(t),

 y = y(t),

 and z = t.

 If the system is inconsistent, enter INCONSISTENT.)

(x, y, z) =

 

 

Answer 1

x + y + z = 4

y - 3z = 11

2x + y + 5z = -5

eq1 - eq2: x + 4z = -7

eq3 - eq2: 2x + 8z = -16 ---> x + 4z = -8

the system is inconsistent.

there is no solution.

checking by Gaussian elimination...

the matrix is:

1 1 1 4

0 1 -3 11

2 1 5 -5

row3 = -2 * row1 + row3

------------------------

1 1 1 4

0 1 -3 11

0 -1 3 -13

row3 = row 2 + row3

--------------------

1 1 1 4

0 1 -3 11

0 0 0 -2