Question

Use the Gauss-Jordan reduction to solve the following linear system:

x1-x2+5x3=-4

5x1-4x2+3x3=-9

2x1 -34x3=14

Answer #1

augmented matrix is

1 | -1 | 5 | -4 |

5 | -4 | 3 | -9 |

2 | 0 | -34 | 14 |

convert into Reduced Row Eschelon Form...

Add (-5 * row1) to row2

1 | -1 | 5 | -4 |

0 | 1 | -22 | 11 |

2 | 0 | -34 | 14 |

Add (-2 * row1) to row3

1 | -1 | 5 | -4 |

0 | 1 | -22 | 11 |

0 | 2 | -44 | 22 |

Add (-2 * row2) to row3

1 | -1 | 5 | -4 |

0 | 1 | -22 | 11 |

0 | 0 | 0 | 0 |

Add (1 * row2) to row1

1 | 0 | -17 | 7 |

0 | 1 | -22 | 11 |

0 | 0 | 0 | 0 |

there is no pivot entry at third column so find the general solution .

........free variable

general solution .is

Add (-2 * row1) to row3

solve the following linear system by gauss-jordan
method
x1 + x2 - 2x3 + x4 = 8
3x1 - 2x2 - x4 = 3
-x1 + x2 - x3 + x4 = 2
2x1 - x2 + x3 - 2x4 = -3

Solve the system
-2x1+4x2+5x3=-22
-4x1+4x2-3x3=-28
4x1-4x2+3x3=30
a)the initial matrix is:
b)First, perform the Row Operation 1/-2R1->R1. The resulting
matrix is:
c)Next perform operations
+4R1+R2->R2
-4R1+R3->R3
The resulting matrix is:
d) Finish simplyfying the augmented mantrix down to reduced row
echelon form. The reduced matrix is:
e) How many solutions does the system have?
f) What are the solutions to the system?
x1 =
x2 =
x3 =

Determine if the linear transformation is (a) one-to-one, (b)
onto.
T(x1,x2,x3)=(2x1 −4x2,x1 −x3,−x2 +3x3).

Find the fundamental system of solutions to the system.
2x1 − x2 + 3x3 + 2x4
+ x5 = 0
x1 + 4x2 − x4 + 3x5
= 0
2x1 + 6x2 − x3 + 5x4
= 0
5x1 + 9x2 + 2x3 +
6x4 + 4x5 = 0.

Consider the following system of equations.
x1- x2+ 3x3 =2
2x1+ x2+ 2x3 =2
-2x1 -2x2 +x3 =3
Write a matrix equation that is equivalent to the system of
linear equations.
(b) Solve the system using the inverse of the coefficient
matrix.

Use Gaussian elimination to solve the following system of linear
equations.
2x1 -2x2 -x3
+6x4 -2x5=1
x1 - x2
+x3 +2x4 - x5=
2
4x1 -4x2
-5x3 +7x4
-x5=6

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) =
()

Consider the following system of equations:
2x1 + 8x2 = 2
x1 + x2 = 4
a) Express the system in the matrix form: Ax = b
b) Showing all work, solve the equations for x1 and
x2 using Gauss-Jordan method
c) Showing all work, solve the equations for x1 and
x2 using Cramer’s Rule
d) Showing all work, solve the equations for x1 and
x2 using the method of Matrix Inversion

Solve The LP problem using the graphic method
Z Max=5X1+3X2
Constaint function:
2X1 + 4X2 ≤ 80
5X1 + 2X2 ≤ 80
X1≥ 0 , X2≥0

Use Gauss
Elimination with partial pivoting method to find x1, x2,and x3 for
the following set of linear equations. You should show all your
work in details. Verify your solutions
2X1
+ X2 - X3 = 1
5X1
+ 2X2 + 2X3 = -4
3X1
+ X2 + X3 = 5

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