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Linear Algebra

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Moderate

3x3 LU with a Zero Entry

LINALG-BYLOEV

Suppose $A$ is a $3\times3$ matrix with entries $(a_{ij})$ and that $A=LU$ is an LU factorization of $A$ without partial pivots.

If the top-left entry of $L$ is zero, what is true of $A$?

A

$A$ is invertible

B

$A$ is upper triangular

C

$A$ is lower triangular

D

All first row entries of $A$ equal $0$

E

All first column entries of $A$ equal $0$