Numerical Analysis/LU decomposition concept quiz

Choose the best answer for each question:

<quiz display=simple> {The LU decomposition is |type="()"} - 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

{Is it true that any matrix can be factorized to LU form without pivoting? |type="()"} - Yes + No

{If A = LU then, det(a) equals: |type="()"} - -det(L)*det(U) + $(l_{11}*l_{22}*...*l_{nn})*(u_{11}*u_{22}*...*u_{nn})$ - Cannot say anything - None of those

{The computational cost of the LU decomposition of an $n\times n$ matrix is: |type="()"} -O($n^2$) -O($n^3$) +O($n^3/3$) -O($n^{1/2}$)

{The number of operations to solve Ax=b when we know L, U is |type="()"} +O($2n^2$) -O($n^3$) -O($n$) -O($n^{1/2}$) </quiz>