Q34

MSQ2 marks

Consider a system of linear equations $P X=Q$ where $P \in \mathbb{R}^{3 \times 3}$ and $\mathrm{Q} \in \mathbb{R}^{3 \times 1}$ . Suppose $P$ has an LU decomposition, $P=L U$ , where

L=\left[\begin{array}{ccc} 1 & 0 & 0 \\ l_{21} & 1 & 0 \\ l_{31} & l_{32} & 1 \end{array}\right] \text { and } U=\left[\begin{array}{ccc} u_{11} & u_{12} & u_{13} \\ 0 & u_{22} & u_{23} \\ 0 & 0 & u_{33} \end{array}\right] \text {. }

Which of the following statement(s) is/are TRUE?

(A)

The system $P X=Q$ can be solved by first solving $L Y=Q$ and then $U X=Y$ .

(B)

If $P$ is invertible, then both $L$ and $U$ are invertible.

(C)

If $P$ is singular, then at least one of the diagonal elements of $U$ is zero.

(D)

If $P$ is symmetric, then both $L$ and $U$ are symmetric.

Loading…