Question

BY USING SUBSTITUTION OR ELIMINATION, which of the following systems are linearly dependent and which are inconsistent?

a.

2x + y - z = 10

4y + 2z = 4

x = 0

b.

-y + z = 0

4x + 2y - z/3 = 0

x + z = 0

c.

-3x + 2y - z = 14

-x - y - z = 0

x + 10y - 3z = 2

Answer #1

Solve each system by elimination.
1) -x-5y-5z=2
4x-5y+4z=19
x+5y-z=-20
2) -4x-5y-z=18
-2x-5y-2z=12
-2x+5y+2z=4
3) -x-5y+z=17
-5x-5y+5z=5
2x+5y-3z=-10
4) 4x+4y+z=24
2x-4y+z=0
5x-4y-5z=12
5) 4r-4s+4t=-4
4r+s-2t=5
-3r-3s-4t=-16
6) x-6y+4z=-12
x+y-4z=12
2x+2y+5z=-15

Use
Gaussian Elimination to solve and show all steps:
1. (x+4y=6)
(1/2x+1/3y=1/2)
2. (x-2y+3z=7)
(-3x+y+2z=-5)
(2x+2y+z=3)

1. Solve by via Gauss-Jordan elimination:
a) 2y + 3z = 8
2x + 3y + z =
5
x − y − 2z =
−5
b) x + 3y + 2z = 5
x −
y + 3z = 3
3x + y + 8z = 10
c) 3x1 + x2 + x3 + 6x4 = 14
x1 − 2x2 +
5x3 − 5x4 = −7
4x1 + x2 + 2x3 + 7x4 =
17

Solve the sytem using elimination. Do not use augmentive
matrix.
(a) 3x - 2y + z = 2
(b) 5x + y - 2z = 1
(c) 4x - 3y + 3z = 7

Solve using elimination method:
x-2y+3z =4
2x-y+z = -1
4x + y + z = 5
What is z in the solution?

Use Gauss-Jordan method (augmented matrix method) to
solve the following systems of linear equations. Indicate whether
the system has a unique solution, infinitely many solutions, or no
solution. Clearly write the row operations you use. (a) (5 points)
x + y + z = 6 2x − y − z = 3 x + 2y + 2z = 0 (b) (5 points) x − 2y
+ z = 4 3x − 5y + 3z = 13 3y − 3z =...

Which of the following systems of equations have nonzero
solutions? If the solution is not unique, give the set of all
possible solutions.
a)3x+4y=0 b)4x-y=0 c)2x-6y=0
6x+2y=0 4x-y=0 -x+3y=-2

Consider the following linear system:
x + 2y + 3z = 6
2x - 3y + 2z = 14
3x + y - z = -2
Use Gaussian Elimination with Partial Pivoting to
solve a solution in an approximated sense.

Solve the system using Gaussian elimination. State whether the
system is? independent, dependent, or inconsistent.
3x-y+2z=5
x+y-4z=6

Use Gaussian elimination with backward substitution to solve the
system of linear equations.
x+y-z=-4
-x-4y+4z=1
-4x-3y+2z=15
What is the solution set?

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