NIELIT 2022 April Scientist B | Section B | Question: 80

Question

The upper triangular matrix $\text{U}$ in the $\text{LU-}$ decomposition of the matrix given below :

$\begin{bmatrix} 1 & -2 & 3 \\  2 & -5  & 8 \\  1 & 2 & -10 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \\  l_{31} & 1  & 0 \\  l_{31} & l_{32} & 1 \end{bmatrix} \begin{bmatrix} u_{11} & u_{12} & u_{13} \\  0 & u_{22}  & u_{23} \\  0 & 0 & u_{33} \end{bmatrix}$ is :

• A. $\begin{bmatrix} 1 & 0 & 0 \\  2 & 1  & 0 \\  1 & -4 & 1 \end{bmatrix}$
• B. $\begin{bmatrix} 1 & -2 & 3 \\  0 & 1  & -6 \\  0 & 0 & 1 \end{bmatrix}$
• C. $\begin{bmatrix} 1 & -2 & 3 \\  0 & -1  & 6 \\  0 & 0 & 11 \end{bmatrix}$
• D. $\begin{bmatrix} 1 & -2 & 3 \\  0 & -1  & 6 \\  0 & 0 & 10 \end{bmatrix}$

Comments

@soujanyareddy13 please recheck the options given, the answer won’t match. The correct option must be:

$\begin{bmatrix} 1 & -2 & 3 \\ 2 & -5 & 8 \\ 1 & 2 & -10 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 1 & -4 & 1 \end{bmatrix} \begin{bmatrix} 1 & -2 & 3 \\ 0 & -1 & 2 \\ 0 & 0 & -5 \end{bmatrix}$.

 

Also there is one more typo in the question $l_{31}$ is used at the place of $l_{21}$.

Answer 1

option D