Question

The value of $\left| \begin{matrix} 265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181 \end{matrix} \right|$ is equal to.

• A. 0
• B. 679
• C. 779
• D. 1000

Answer 1

Answer: (A)

0

Answer 2

$\left| \begin{matrix} 265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181 \end{matrix} \right| = \left| \begin{matrix} 25 & 21 & 219 \\ 15 & 27 & 198 \\ 21 & 17 & 181 \end{matrix} \right|$

{Applying $C_{1} \rightarrow C_{1} - C_{2};C_{2} \rightarrow C_{2} - C_{3}\}$

=$\left| \begin{matrix} 4 & 21 & 9 \

• 12 & 27 & - 72 \ 4 & 17 & 11 \end{matrix} \right|$

{Applying $C_{1} \rightarrow C_{1} - C_{2};C_{3} \rightarrow C_{3} - 10C_{2}\}$

= $\left| \begin{matrix} 4 & 21 & 9 \

• 12 & 27 & - 72 \ 0 & - 4 & 2 \end{matrix} \right|{ApplyingR_{3} \rightarrow R_{3} - R_{1}$}

=$4\left| \begin{matrix} 1 & 21 & 9 \

• 3 & 27 & - 72 \ 0 & - 4 & 2 \end{matrix} \right| = 4\left| \begin{matrix} 1 & 21 & 9 \ 0 & 90 & - 45 \ 0 & - 4 & 2 \end{matrix} \right|$by$R_{2} \rightarrow 3R_{1} + R_{2}$

= $2X = \begin{bmatrix} 3 & 2 \\ 0 & - 2 \end{bmatrix} + \begin{bmatrix} 1 & 2 \\ 7 & 4 \end{bmatrix} \Rightarrow 2X = \begin{bmatrix} 4 & 4 \\ 7 & 2 \end{bmatrix}$= 0.