The matrix [A] = 214-1 is decomposed into a product of a

The matrix [A] = 2 1
4 -1

is decomposed into a product of a lower triangular matrix [L] and an upper triangular matrix [U]. The properly decomposed [L] and [U] matrices respectively are

By Dolittle’s decomposition,

		2			1		=		1			0			u₁₁			u₁₂
		4			-1		=		l₂₁			1			0			u₂₂

We have u₁₁ = 2, u₁₂ = 1
l₂₁ u₁₁ = 4
⇒ l₂₁ = 2
and l ₂₁u₁₂ + u₂₂ = – 1
⇒ u₂₂ = – 1 – l ₂₁u₁₂ = – 3

then ,		2			1		=		1			0			2			1		.......(A)
then ,		4			-1		=		2			1			0			-3		.......(A)

eqn (A) does not signfy any choice
Now, from crout’s decomposition,

		2			1		=		l₁₁			0			1			u₁₂
		4			-1		=		l₂₁			l₂₂			0			1

We get, l₁₁ = 2, l₁₁ u₁₂ = 1

u₁₂ =	1	= 0.5
	2

and, l ₂₁ = 4 , l₂₁ u₁₂ + l₂₂ = – 1
⇒ l₂₂ = – 3

Then ,		2			1		=		2			0			1			0.5
Then ,		4			-1		=		4			-3			0			1

Hence the choice is (d).