GATE 2018 MA LU DECOMPOSITION

Question

Answer 1

$P:$ Given that $A=\begin{bmatrix} 0&5 \\0 & 7\end{bmatrix}$

             If this matrix have LU-decomposition, then $|A|_{1\times1}\neq0$ and $|A|_{2\times2}\neq0$

              Here $|A|_{1\times1}=0$  and $|A|_{2\times2}=0$

  So, this is not LU-decomposition.

$Q:$ Given that $B=\begin{bmatrix} 0&0 \\2 & 5\end{bmatrix}$

             If this matrix have LU-decomposition, then $|B|_{1\times1}\neq0$ and $|B|_{2\times2}\neq0$

              Here $|B|_{1\times1}=0$  and $|B|_{2\times2}=0$

  So, this is not LU-decomposition.

So, $P$ False and $Q$ are True.

Comments

Q is true.

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Thanks, I miss read the Q option.