The-factors-of-determinant-x-a-b-a-x-b-a-b-x-are-

Question Number 21174 by akinyeni last updated on 15/Sep/17

The factors of | \begin{matrix} x & a & b \\ a & x & b \\ a & b & x \end{matrix} | are

Answered by $@ty@m last updated on 15/Sep/17

= | \begin{matrix} x & a & b \\ 0 & x - b & b - x \\ a & b & x \end{matrix} |, b y R_{2} \to R_{2} - R_{3}

= (x - b) | \begin{matrix} x & a & b \\ 0 & 1 & - 1 \\ a & b & x \end{matrix} |

= (x - b) | \begin{matrix} x & a + b & b \\ 0 & 0 & - 1 \\ a & b + x & x \end{matrix} |, b y C_{2} \to C_{2} + C_{3}

= (x - b) | \begin{matrix} x & a + b \\ a & b + x \end{matrix} |

= (x - b) | \begin{matrix} x - a & a - x \\ a & b + x \end{matrix} |, b y R_{1} \to R_{1} - R_{2}

= (x - b) (x - a) | \begin{matrix} 1 & - 1 \\ a & b + x \end{matrix} |

= (x - a) (x - b) | \begin{matrix} 0 & - 1 \\ a + b + x & b + x \end{matrix} |, b y C_{1} \to C_{1} + C_{2}

= (x - a) (x - b) (a + b + x)

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