Question

Consider the following system of linear equations:

2x_{1}−2x_{2}+4x_{3} |
= | −10 |

x_{1}+x_{2}−2x_{3} |
= | 5 |

−2x_{1}+x_{3} |
= | −2 |

Let A be the coefficient matrix and X the solution matrix to the
system. Solve the system by first computing A^{−1} and then
using it to find X.

You can resize a matrix (when appropriate) by clicking and dragging
the bottom-right corner of the matrix.

Answer #1

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.

Solve the following system of linear equations: 3x2−9x3 = −3
x1−2x2+x3 = 2 x2−3x3 = 0 If the system has no solution, demonstrate
this by giving a row-echelon form of the augmented matrix for the
system. If the system has infinitely many solutions, your answer
may use expressions involving the parameters r, s, and t. You can
resize a matrix (when appropriate) by clicking and dragging the
bottom-right corner of the matrix.

Consider the following system of equations.
x1+2x2+2x3 −
2x4+2x5 = 5
−2x1 − 4x3+ x4 −
10x5 = −11
x1+2x2 − x3+3x5 =
4
1. Represent the system as an augmented matrix.
2. Reduce the matrix to row reduced echelon form. (This can be
accomplished by hand or by MATLAB. No need to post code.)
3. Write the set of solutions as a linear combination of vectors
in R5. (This must be accomplished by hand using the rref
form found...

Duality Theory: Consider the following LP:
max 2x1+2x2+4x3
x1−2x2+2x3≤−1
3x1−2x2+4x3≤−3
x1,x2,x3≤0
Formulate a dual of this linear program. Select all the correct
objective function and constraints
1. min −y1−3y2
2. min −y1−3y2
3. y1+3y2≤2
4. −2y1−2y2≤2
5. 2y1+4y2≤4
6. y1,y2≤0

3. Consider the system of linear equations
3x1 + x2 + 4x3 − x4
= 7
2x1 − 2x2 − x3 + 2x4
= 1
5x1 + 7x2 + 14x3 −
8x4 = 20
x1 + 3x2 + 2x3 + 4x4
= −4
b) Solve this linear system applying Gaussian forward
elimination with partial pivoting and back ward substitution, by
hand. In (b) use fractions throughout your calculations.
(i think x1 = 1, x2= -1, x3 =1,
x4=-1, but i...

by hand, solve the system of equations- LU Factorization
-3x1+x2+x3=-2
x1+x2-x3=1
2x1+x2-2x3=1

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

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

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 3x3 system.
x1-x2+x3=3
-2x1+3x2+2x3=7
3x1-3x2+2x3=6

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