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

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

Can you answer this question?

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

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

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

$\qquad\qquad\quad=18$

answered Feb 20, 2013
edited Feb 24, 2013