Numerical Analysis/LU decomposition concept quiz

Choose the best answer for each question:

1 The LU decomposition is

	The name of an algorithm to solve a linear system.
	A matrix decomposition which writes a matrix as the product of a lower triangular matrix and an upper triangular matrix.
	The same as a QR decomposition.
	None of those

2 Is it true that any matrix can be factorized to LU form without pivoting?

	Yes
	No

3 If A = LU then, det(a) equals:

	-det(L)*det(U)
	$(l_{11}*l_{22}*...*l_{nn})*(u_{11}*u_{22}*...*u_{nn})$
	Cannot say anything
	None of those

4 The computational cost of the LU decomposition of an $n\times n$ matrix is:

	O($n^{2}$)
	O($n^{3}$)
	O($n^{3}/3$)
	O($n^{1/2}$)

5 The number of operations to solve Ax=b when we know L, U is

	O($2n^{2}$)
	O($n^{3}$)
	O($n$)
	O($n^{1/2}$)