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# Evaluate the determinant:$\begin{vmatrix} 2&4 \\ -5&-1 \end{vmatrix}$

$\begin{array}{1 1} -22 \\ 18 \\ -18 \\ 22 \end{array}$

Toolbox:
• $\mid A\mid$ of $\begin{vmatrix}a_{11} & a_{12}\\a_{21} & a_{22}\end{vmatrix}=a_{11}a_{22}-a_{21}a_{12}$
• To evaluate the value of the given determinants ,let us multiply the elements $a_{11}$ and $a_{22}$ and then subtract $a_{21}\times a_{12}$.

Given:Evaluate:$\begin{vmatrix}2 & 4\\-5 & -1\end{vmatrix}$

To evaluate this we know we will have to multiply the elements of the first diagonal and subtract with the elements multiplied along the other diagonal,since it is of order two.

(i.e)$a_{11}a_{22}-a_{21}a_{12}$

Here $a_{11}=2$

$a_{22}=1$

$a_{21}=-5$

$a_{12}=4$

Therefore $\mid A\mid=2\times -1-(-5)\times 4.$

$\qquad\qquad\quad=-2-(-20)$

$\qquad\qquad\quad=-2+20$

$\qquad\qquad\quad=18$

edited Feb 24, 2013