Numerical Analysis/LU decomposition concept quiz

< Numerical Analysis

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})

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