Show that the value of the following determinant is zero- 1 43 6 7 35 4 3 17 2

1 amp; 43 amp; 6 7 amp; 35 amp; 4 3 amp; 17 amp; 2 Expanding the determinant, we get =1(70 68) 43(14 12)+6(119 105) ...

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Standard XII

Mathematics

Definition of a Determinant

Show that the...

Question

Show that the value of the following determinant is zero:
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 43 & 6 7 & 35 & 4 3 & 17 & 2 \end{matrix} ∣ ∣ ∣ ∣$

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Solution

$∣ ∣ ∣ ∣ \begin{matrix} 1 & 43 & 6 7 & 35 & 4 3 & 17 & 2 \end{matrix} ∣ ∣ ∣ ∣$

Expanding the determinant, we get

$= 1 (70 - 68) - 43 (14 - 12) + 6 (119 - 105)$

$= 2 - 86 + 84$

$= 0$

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Show that the value of the following determinant is zero: ∣∣ ∣∣143673543172∣∣ ∣∣

∣∣ ∣∣143673543172∣∣ ∣∣Expanding the determinant, we get=1(70−68)−43(14−12)+6(119−105)=2−86+84=0

Show that the value of the following determinant is zero:
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 43 & 6 7 & 35 & 4 3 & 17 & 2 \end{matrix} ∣ ∣ ∣ ∣$

$∣ ∣ ∣ ∣ \begin{matrix} 1 & 43 & 6 7 & 35 & 4 3 & 17 & 2 \end{matrix} ∣ ∣ ∣ ∣$

Expanding the determinant, we get

$= 1 (70 - 68) - 43 (14 - 12) + 6 (119 - 105)$

$= 2 - 86 + 84$

$= 0$