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Inverse of a Matrix

Find the volu...

Question

Find the volume of the parallelopiped whose coterminous edges are represented by $a = 2 i - 3 j + 4 k, b = i + 2 j - k, c = 3 i - j + 2 k$

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Solution

Volume $= ∣ ∣ ∣ ∣ \begin{matrix} 2 & - 3 & 4 1 & 2 & - 1 3 & - 1 & 2 \end{matrix} ∣ ∣ ∣ ∣$
$= 2 (4 - 1) + 3 (2 + 3) + 4 (- 1 - 6)$
$= 6 + 15 - 28 = | - 7 | = 7$

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¯ ¯ ¯ a = 3 ¯ i - ¯ j + 4 ¯ ¯ ¯ k, ¯ ¯ b = 2 ¯ i + 3 ¯ j - ¯ ¯ ¯ k

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λ

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[\vec{a} \vec{b} \vec{c}]

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