LU decomposition

Question

Given the system of linear equations:

$4y\ +\ 3z\ =\ 8\\ 2x\ -\ z\ =\ 2\\ 3x\ +\ 2y\ =\ 5$

Find L & U.

Comments

LU decomposition is done on matrix. Matrix is not given.

Answer 1

AX=B

A=LU....

NOw Here

$\begin{bmatrix} 0 &4 &3 \\ 2 &0 &-1 \\ 3&2 & 0 \end{bmatrix}$....

For finding LU decomposition of a matrix A...is possible IFF all leading det(A) must be non-zero...det(1,1) is zero...

Comments

Can't we interchange the rows?

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here leading  principal minors are not 0 pls check.

Answer 2

LU Decomposition is done on non singular matrix . It is singular so here it is not valid.