Rank of a matrix $\left[\begin{array}{cccc}5 & 3 & -3 & -1 \\ 3 & 2 & -2 & -1 \\ 2 & -1 & 2 & 8\end{array}\right]$ is

(A) 1

(B) 2

(C) 3

(D) 4

Rank of a matrix $\left[\begin{array}{cccc}5 & 3 & -3 & -1 \\ 3 & 2 & -2 & -1 \\ 2 & -1 & 2 & 8\end{array}\right]$ is

(A) 1

(B) 2

(C) 3

(D) 4

A particle is subjected to forces $\mathbf{P}=2 \mathbf{i}-5 \mathbf{j}+6 \mathbf{k}$ and $\mathbf{Q}=-\mathbf{i}+2 \mathbf{j}-\mathbf{k} .$ The positional vectors are $\overrightarrow{O A}=4 \mathbf{i}-3 \mathbf{j}-2 \mathbf{k}$ and $\overrightarrow{O B}=6 \mathbf{i}+\mathbf{j}-3 \mathbf{k}$. Work done by the resultant force $(\mathbf{F}=\mathbf{P}+\mathbf{Q})$ to move the particle from $\mathrm{A}$ to $\mathrm{B}$ is

(A) 2

(B) -5

(C) 12

(D) -15

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