# 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) ${\displaystyle (l_{11}*l_{22}*...*l_{nn})*(u_{11}*u_{22}*...*u_{nn})}$ Cannot say anything None of those

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

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

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

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