Question

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

Answer #1

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...

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

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

Consider the following integer programming problem.Maximize:
z=8x1 +12x2 +6x3
+4x4
Subject to constraint: 5x1 + 9x2
+4x3 +3x4 ≤ 16 where x1, x2, x3 and x4 are
binary integers (0 or 1).
By applying the Branch and Bound Algorithm find the
solution.

in parts a and b use gaussian elimination to solve the systems
of linear equations. show all steps.
a. x1 - 4x2 - x3 + x4 = 3
3x1 - 12 x2 - 3x4 = 12
2x1 - 8x2 + 4x3 - 10x4 = 12
b. x1 + x2 + x3 - x4 = 2
2x1 + 2x2 - 2x3 = 3
2x1 + 2x2 - x4 = 2

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

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...

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 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.

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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