Given that the determinant of the matrix - 2 6 0- 4 12 8- -2 0 4 - is - 96- the determinant of the matrix - 4 12 0- 8 24 16- -4 0 8 - is

(d) nbsp; D = 96 for the given matrix (Traking 2 common from each row) ∴ nbsp; nbsp; nbsp; nbsp; nbsp;Det (A) = (2)^3× D =8× ( 96)= 768 ...

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Engineering Mathematics

Determinant Properties-1

Given that th...

Question

$Given that the determinant of the matrix ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & 0 4 & 12 & 8 - 2 & 0 & 4 \end{matrix} ⎤ ⎥ ⎦ is - 96, the determinant of the matrix ⎡ ⎢ ⎣ \begin{matrix} 4 & 12 & 0 8 & 24 & 16 - 4 & 0 & 8 \end{matrix} ⎤ ⎥ ⎦ is$

- 192

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384

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-384

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- 768

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Solution

The correct option is D - 768
(d)
D = -96 for the given matrix
(Traking 2 common from each row)
$∴$ $D e t (A) = (2)^{3} \times D$
$= 8 \times (- 96) = - 768$

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Given that the determinant of the matrix ⎡⎢⎣2604128−204⎤⎥⎦ is - 96, the determinant of the matrix ⎡⎢⎣412082416−408⎤⎥⎦ is

The correct option is D - 768(d) D = -96 for the given matrix (Traking 2 common from each row) ∴ Det(A)=(2)3×D =8×(−96)=−768

$Given that the determinant of the matrix ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & 0 4 & 12 & 8 - 2 & 0 & 4 \end{matrix} ⎤ ⎥ ⎦ is - 96, the determinant of the matrix ⎡ ⎢ ⎣ \begin{matrix} 4 & 12 & 0 8 & 24 & 16 - 4 & 0 & 8 \end{matrix} ⎤ ⎥ ⎦ is$

The correct option is D - 768
(d)
D = -96 for the given matrix
(Traking 2 common from each row)
$∴$ $D e t (A) = (2)^{3} \times D$
$= 8 \times (- 96) = - 768$