Compute the LU factorization of each of the following matrices. begin{bmatrix}2 & 4 -2 & 1 end{bmatrix}

Reggie 2020-11-09 Answered
Compute the LU factorization of each of the following matrices.
[2421]
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Expert Answer

grbavit
Answered 2020-11-10 Author has 109 answers
Step 1 : Given:
A matrix [2421] We have to compute the LU factorization of this matrix.
Step 2 : Formula Used
LU Factorization: If we have a matrix A, then an upper triangular matrix U obtained without pivoting under Gaussian elimination method, and there exists lower triangular matrix L s.t. A = LU.
Step 3: Calculation
[2421]
Use Gaussian Eliminatin Method , R2R2(1)R1
[2405]
U=[2405]
Now , use gaussian elimination with 1st column , we get
[1011]
L=[1011]
Hence,
[2421]=[1011][2405]=LU
This is the LU factorization of the given matrix.
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