Compute the LU factorization of each of the following matrices. [−21241−2−6−34]

Dottie Parra

Dottie Parra

Answered question


Compute the LU factorization of each of the following matrices.

Answer & Explanation

Arham Warner

Arham Warner

Skilled2021-06-01Added 102 answers

Step 1
Given: Matrix
To find: LU decomposition of the given matrix
Procedure: We are trying to find two matrices L and U such that A = LU
Here, L is a lower triangular matrix whose all diagonal entries are 1 and entries above the main diagonal are 0
Similarly, U is an upper triangular matrix whose all entries below the main diagonal are 0
Hence we start by finding U, by making entries below main diagonal 0 using row operations and then we will find L using opposites of the multiples used in building U
Note that L is of the form:
Step 2
Computation of U and L
We need to make entry in the first column below -2 as 0
Apply row operation to get second row of U: R22R1+R2 and now the multiplier is 2 and so we get -2 below first main diagonal element of L
Now we want to get 0 in place of -6 in the first column
Apply row operation, R33R1+R3 and now the multiplier is -3, hence we get 3 below the entry -2 in L
Call the matrix obtained from A by applying row operations as U
Step 3

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