Q: (LU decomposition) Find the LU decomposition of A = [-3 2 5
1; 12 -4 -20 -2; -6 0 15 1; -9 6 35 4]. You can use the compact
method which works within a single matrix or you can build L and U
separately. State L and U explicitly, and verify (in Matlab) that A
= L*U. Hint: Matlab's built-in lu function isn't useful, since it
pivots.
Solve the following set of equations with LU factorization with
pivoting:
3x1 -2x2 + x3 = -10
2x1 + 6x2- 4x3 = 44
-8x1 -2x2 + 5x3 = -26
Please show all steps
4. (Applying LU and LUP decompositions) In this problem, we'll
use the LU/LUP decomposition to solve a linear system of
equations.
a) For A = [12 -8 13 -1 13;14 11 -5 -5 -7;1 -8 -9 10 8;-11 10 -8
3 8;-11 -8 4 2 -4] find matrices P, L, and U so that PA = LU using
Matlab's lu function. Based on your results: did Matlab use
pivoting during the lu-computation?
b) For b = [4;-4;-5;3;7] solve Ax =...
Consider the following LP model.Max Z = 3x1 - 4x2 +
x3
subject to x1 + x2 + x3 >= 9
2x1
+ x2 + x3<= 12
x1 + x2 = 5
x1, x2, x3 >= 0
Change it to standard form.
Obtain all the basic solutions and indicate which ones are basic
feasible solutions and write down the corresponding corner points.
For each basic solution, you have to obtain the values of all the
variables.
Obtain the solution of the LP...
For the system
2x1 − 4x2 + x3 + x4 = 0,
x1 − 2x2 + 5x4 = 0,
find some vectors v1, . . . , vk such that the solution set to
this system equals span(v1, . . . , vk).
Solve the following systems of equation using the formula by
Cramer and with the inverse matrices.
4x1 - x2 + 2x3 = 8
-x1 + 2x2 = -7
x1 - 3x2 - 5x3 = 2
Use LU decomposition to solve the following system of equations
(show your work). Do not use a pivoting strategy, and check your
results by using the matrix inverse to show that [A][A]-1= [I].
8x+ 2y−z=10
- 2x+4y+z=5
3x−y+ 6z=7