Question

5 2 2 - 3 Find the value of the determinant 2 -3 6
3 -4 -11
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Answer 1

SOLUTION

CORRECT QUESTION

Find the value of the determinant

$\displaystyle \sf \begin{vmatrix} 2 & - 3 & 6\\ 3 & - 4 & - 11 \\ 5 & 2 & 4 \end{vmatrix}$

EVALUATION

Here the given determinant is

$\displaystyle \sf \begin{vmatrix} 2 & - 3 & 6\\ 3 & - 4 & - 11 \\ 5 & 2 & 4 \end{vmatrix}$

We find the value of the determinant as below

$\displaystyle \sf \begin{vmatrix} 2 & - 3 & 6\\ 3 & - 4 & - 11 \\ 5 & 2 & 4 \end{vmatrix}$

On expansion we get

$\displaystyle \sf \begin{vmatrix} 2 & - 3 & 6\\ 3 & - 4 & - 11 \\ 5 & 2 & 4 \end{vmatrix}$

$\displaystyle \sf = 2[( - 4 \times 4) - ( - 11 \times 2)] + 3[( 3 \times 4) - ( - 11 \times 5)] + 6[( 3 \times 2) - ( - 4 \times 5)]$

$\displaystyle \sf = 2[ - 16 + 22] + 3[12 + 55] + 6[6 + 20]$

$\displaystyle \sf =12 + 201 + 156$

$\displaystyle \sf = 369$

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