Question

Solve using Gaussian Elimination with back subsitution:

3x(1) - 2x(2) + x(3) =3

2x(1) + 4x(2) - 2x(3) = 2

4x(1) - 2x(2) - 3x(2) = -12

Answer #1

system is

augmented matrix is

3 | -2 | 1 | 3 |

2 | 4 | -2 | 2 |

4 | -2 | -3 | -12 |

convert into Row Eschelon Form...

Divide row1 by 3

1 | -2/3 | 1/3 | 1 |

2 | 4 | -2 | 2 |

4 | -2 | -3 | -12 |

Add (-2 * row1) to row2

1 | -2/3 | 1/3 | 1 |

0 | 16/3 | -8/3 | 0 |

4 | -2 | -3 | -12 |

Add (-4 * row1) to row3

1 | -2/3 | 1/3 | 1 |

0 | 16/3 | -8/3 | 0 |

0 | 2/3 | -13/3 | -16 |

Divide row2 by 16/3

1 | -2/3 | 1/3 | 1 |

0 | 1 | -1/2 | 0 |

0 | 2/3 | -13/3 | -16 |

Add (-2/3 * row2) to row3

1 | -2/3 | 1/3 | 1 |

0 | 1 | -1/2 | 0 |

0 | 0 | -4 | -16 |

Divide row3 by -4

1 | -2/3 | 1/3 | 1 |

0 | 1 | -1/2 | 0 |

0 | 0 | 1 | 4 |

from the last row

from the second row

.

.

from the first row

.

.

.

solution is

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)

solve the equations
a). 4x-(-3x-3) =2x +1-1/2x+1
b) 8x-x^2=2 solvee by completing square
c) x-2x^2=5 solve by quadraticformula

Consider the linearly independent set of vectors
B= (-1+2x+3x^2+4x^3+5x^4, 1-2x+3x^2+4x^3+5x^4,
1+2x-3x^2+4x^3+5x^4, 1+2x+3x^2-4x^3+5x^4, 1+2x+3x^3+4x^3-5x^4)
in P4(R), does B form a basis for P4(R) and why?

Use either Gaussian Elimination with back substituting or
Gauss-Jordan Elimination to solve the system:
−?1 + ?2 + 2?3 = 1 2?1 + 3?2 + ?3 = −2 5?1 + 4?2 + 2?3 = 4

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

Solve the system using either Gaussian elimination with
back-substitution or Gauss-Jordan elimination. (If there is no
solution, enter NO SOLUTION. If the system has an infinite number
of solutions, express x1,
x2, and x3 in terms of the
parameter t.)
2x1
+
3x3
=
3
4x1
−
3x2
+
7x3
=
4
8x1
−
9x2
+
15x3
=
13
(x1,
x2, x3) =
()

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

solve for x using the factor theorem and long division. a.
2x^3-3x^2-5x+6=0 b. 8x^3+4x^2-18x-9=0 c.
2x^3+10x^2+13x+5=0 d. -2x^3-12x^2+x+60=0

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

Solve the system of equations using matrices. Use the Gaussian
elimination method with back-substitution.
{3a - b -3c = 13
{2a - b + 5c = -5
{a + 2b - 5c = 10
Use the Gaussian elimination method to obtain the matrix in
row-echelon form. Choose the correct answer below.
The solution set is {(_,_,_,_)}

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