Question

please answer fast and correctly please​

Answer 1

Step-by-step explanation:

Let the given matrix be

$A = \left[ \begin {array}{ccc}1 & - 1 &2 \\ 3 & 0 & 4 \\ - 4 & - 2 &5 \end{array} \right]$

Now,

$\det{A } = |A| = \left| \begin {array}{ccc}1 & - 1 &2 \\ 3 & 0 & 4 \\ - 4 & - 2 &5 \end{array} \right |$

$\tt \large{\red{ • \: R_{3} \to \: R_{3} - 2 R_{1}}}$

$\implies |A| = \left| \begin {array}{ccc}1 & - 1 &2 \\ 3 & 0 & 4 \\ - 4 - 2 & - 2 + 2 &5 - 4 \end{array} \right |$

$\implies |A| = \left| \begin {array}{ccc}1 & - 1 &2 \\ 3 & 0 & 4 \\ - 6 & 0 &1 \end{array} \right |$

$\tt \large{\red{ • \: Opening \: \: along \: \: C_{2} }}$

$\implies |A| = - ( - 1) \left| \begin {array}{cc} 3 & 4 \\ - 6 &1 \end{array} \right |$

$\implies |A| = 1 \{3 - ( - 6).(4) \}$

$\implies |A| = (3 + 24)$

$\implies |A| = 27$