Find-the-determinant-of-the-matrix-below-determinant-3-1-5-3-4-3-8-5-6-2-1-7-8-5-8-1-

Question Number 9271 by tawakalitu last updated on 27/Nov/16

Find the determinant of the matrix below .

| \begin{matrix} 3 1 5 3 \\ 4 3 8 5 \\ 6 2 1 7 \\ 8 5 8 1 \end{matrix} |

Answered by mrW last updated on 27/Nov/16

C 4 - C 1 :

| \begin{matrix} 3 & 1 & 5 & 0 \\ 4 & 3 & 8 & 1 \\ 6 & 2 & 1 & 1 \\ 8 & 5 & 8 & - 7 \end{matrix} |

C 1 - C 2 \times 3 and C 3 - C 2 \times 5 :

| \begin{matrix} 0 & 1 & 0 & 0 \\ - 5 & 3 & - 7 & 1 \\ 0 & 2 & - 9 & 1 \\ - 7 & 5 & - 17 & - 7 \end{matrix} |

= - | \begin{matrix} - 5 & - 7 & 1 \\ 0 & - 9 & 1 \\ - 7 & - 17 & - 7 \end{matrix} |

= - 1 \times (- 5) (9 \times 7 + 17 \times 1) - 1 \times (- 7) (- 7 \times 1 + 9 \times 1)

= 5 \times 80 + 7 \times 2

= 414

Commented by tawakalitu last updated on 27/Nov/16

Thank for your help . i really appreciate sir .