The-value-of-determinant-determinant-x-2-x-3-x-5-x-4-x-6-x-9-x-8-x-11-x-15-is-

Question Number 70385 by ®Ëƒ ¬Ë°¹¾¨ ‰¦Í¦¿¨ ¸Ë¹Ç² last updated on 04/Oct/19

The value of determinant

| \begin{matrix} x + 2 & x + 3 & x + 5 \\ x + 4 & x + 6 & x + 9 \\ x + 8 & x + 11 & x + 15 \end{matrix} | is

Answered by $@ty@m123 last updated on 04/Oct/19

= | \begin{matrix} - 1 & - 2 & x + 5 \\ - 2 & - 3 & x + 9 \\ - 3 & - 4 & x + 15 \end{matrix} | {\begin{cases} b y C_{1} \to C_{1} - C_{2} \\ & C_{2} \to C_{2} - C_{3} \end{cases}

= | \begin{matrix} 1 & 1 & - 4 \\ 1 & 1 & - 6 \\ - 3 & - 4 & x + 15 \end{matrix} | {\begin{cases} b y R_{1} \to R_{1} - R_{2} \\ & R_{2} \to R_{2} - R_{3} \end{cases}

= | \begin{matrix} 0 & 0 & 2 \\ 1 & 1 & - 6 \\ - 3 & - 4 & x + 15 \end{matrix} | b y R_{1} \to R_{1} - R_{2}

= 2 | \begin{matrix} 1 & 1 \\ - 3 & - 4 \end{matrix} |

= 2 (- 4 + 3)

= - 2