find-the-determinant-of-the-matrix-below-1-4-3-1-2-0-6-3-4-1-2-5-1-0-2-4-

Question Number 9285 by suci last updated on 28/Nov/16

f i n d t h e d e t e r m i n a n t o f t h e m a t r i x b e l o w

[\begin{matrix} 1 & 4 & - 3 & 1 \\ 2 & 0 & 6 & 3 \\ 4 & - 1 & 2 & 5 \\ 1 & 0 & - 2 & 4 \end{matrix}]

Answered by mrW last updated on 28/Nov/16

∣ A ∣= | \begin{matrix} 1 & 4 & - 3 & 1 \\ 2 & 0 & 6 & 3 \\ 4 & - 1 & 2 & 5 \\ 1 & 0 & - 2 & 4 \end{matrix} |

R 4 - R 1 and R 3 - R 2 \times 2 :

∣ A ∣= | \begin{matrix} 1 & 4 & - 3 & 1 \\ 2 & 0 & 6 & 3 \\ 0 & - 1 & - 10 & - 1 \\ 0 & - 4 & 1 & 3 \end{matrix} |

R 2 - R 1 \times 2 :

∣ A ∣= | \begin{matrix} 1 & 4 & - 3 & 1 \\ 0 & - 8 & 12 & 1 \\ 0 & - 1 & - 10 & - 1 \\ 0 & - 4 & 1 & 3 \end{matrix} |

= 1 \times | \begin{matrix} - 8 & 12 & 1 \\ - 1 & - 10 & - 1 \\ - 4 & 1 & 3 \end{matrix} |

R 2 + R 1 :

= 1 \times | \begin{matrix} - 8 & 12 & 1 \\ - 9 & 2 & 0 \\ - 4 & 1 & 3 \end{matrix} |

R 3 - R 1 \times 3 :

= 1 \times | \begin{matrix} - 8 & 12 & 1 \\ - 9 & 2 & 0 \\ 20 & - 35 & 0 \end{matrix} |

= 1 \times 1 \times | \begin{matrix} - 9 & 2 \\ 20 & - 35 \end{matrix} |

= (- 9) \times (- 35) - 2 \times 20 = 275

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