Differentiate the Gaussian elimination and LU- Factorization in solving system of linear equations.

Marvin Mccormick 2021-02-25 Answered
Differentiate the Gaussian elimination and LU- Factorization in solving system of linear equations.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

nitruraviX
Answered 2021-02-26 Author has 101 answers

Let the system of linear equation be
AX=b
Gauss elimination for system of linear equation by back substitution for the system give the upper triangular system of linear equation which is solvable easily.
If we apply Gauss elimination for the matrix of the the system then it gives the equivalent matrix which is the product of two matrices, upper triangular matrix U and Lower triangular matrix L.
i.e.,
A=LU.
then the system is
AX=b
LUX=b
UX=L1b
x=U1(L1b)

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-06-01

Find the linear approximation of the function f(x)=4x at a=0
Use L(x) to approximate the numbers 3.9 and 3.99 Round to four decimal places

asked 2021-09-10

The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y. or x, y, z. or x1,x2,x3,x4 x ​ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [100010001023120]

asked 2021-02-19
For the given a system of linear equations
4x+y-5z=8
-2x+3y+z=12
3x-y+4z=5
Use matrix inversion to solve simultaneous equations.
asked 2021-06-30

Do the equations 4x3y=5 and 7y+2x=8 form a system of linear equations? Explain.

asked 2022-05-21
How to solve this linear pde for y ( x ) (other functions are known and λ is a constant):
d d x ( g ( x ) y ( x ) ) = λ 2 g ( x ) y ( x )
Everything I know about this equation is that it is called the Sturmian equation. I did some research, but the theory, which is for a more general form of the equation, is too hard for me to understand.
asked 2022-06-20
Given that f : is invertible, differentiable and monotonic increasing.
Need to find a general solution for the equation:
f ( y ) y = x f ( y )
I'm working to either separate variables or to put the equation in linear form of y but no success so far.
asked 2022-02-25
Let us have 3 vectors in R3:
(a1,b1,c1),(a2,b2,c2) and (a3,b3,c3)
These vectors are linearly dependent if and only if the following scalar equation holds:
a1(b2c3b3c2)b1(a2c3a3c2)+c1(a2b3a3b2)=0
1. This equation is a necessary and sufficient condition of lineary dependence.
2. This criterion is a scalar equation (not a pair of equations; not a vector form).
3. This equation is a linear equation as to (ai,bi,ci) for all i{1,2,3}.
Now let us have 2 strings in R3:
(a1,b1,c1) and (a2,b2,c2)
Is there a similar way to determine whether this set of vectors in R3 is linearly dependent?
I.e. the way such as the following scalar equation:
f(a1,b1,c1,a2,b2,c2)=0
so, that
1.This equation is a necessary and sufficient condition of linear dependence.
2.This criterion is a scalar equation (not a pair of equations; not a vector form).
3. This equation is a linear equation as to (ai,bi,ci) for all i{1,2}.