Question

by hand, solve the system of equations- LU Factorization

-3x1+x2+x3=-2

x1+x2-x3=1

2x1+x2-2x3=1

Answer #1

**Solution:**

By

By

By

is made up of the multipliers with on the diagonal.

Thus,

Let

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

Solve the following system of equations using LU factorization
with partial pivoting:
2x1 − 6x2 − x3 = −38
−3x1 − x2 + 7x3 = −34
−8x1 + x2 − 2x3 = −40
I would like to write a matlab code to solve the problem without
using loops or if statements. All i want is a code to swap the
rows. I can solve the rest. Thank you in advance.

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.

Consider the following system of linear equations:
2x1−2x2+4x3
=
−10
x1+x2−2x3
=
5
−2x1+x3
=
−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.

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

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...

minimize F=5x1 - 3x2 - 8x3
subject to (2x1 + 5x2 - x3 ≤1)
(-2x1 - 12x2 + 3x3 ≤9)
(-3x1 - 8x2 + 2x3 ≤4)
x1,x2,x3≥0 solve implex method pls.

Solve for all 4-tuples (x1, x2, x3, x4) simultaneously
satisfying the following equations:
8x1 −9x2 −2x3 −5x4 = 100
9x1 +6x2 −6x3 +9x4 = 60
−3x1 −9x2 +4x3 −2x4 = −52
−7x2 +8x3 +8x4 = −135

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

x1-5x2+x3+3x4=1
2x1-x2-3x3-x4=3
-3x1-3x3+7x3+5x4=k
1 ) There is exactly one real number k for which the system has
at least one solution; determine this k and describe all solutions
to the resulting system.
2 ) Do the solutions you found in the previous part form a
linear subspace of R4?
3 ) Recall that a least squares solution to the system of equations
Ax = b is a vector x minimizing the length |Ax=b| suppose that
{x1,x2,x3,x4} = {2,1,1,1}
is a...

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