Question

Find the values of the determinants |5 -2| : : |-3 1|

Answer 1

Here given,
$\left[\begin{array}{cc}5&-2\\-3&1\end{array}\right]$

we know, if any determinant in the form of
$\left[\begin{array}{cc}a_1&a_2\\a_3&a_4\end{array}\right]$
then value of determinant = a₁a₄ - a₂a₃

now, solve above determinant with help of it ,
e.g.,value of given determinant = 5 × 1 - (-2) × (-3) = 5 - 6 = - 1

Answer 2

The value of this determinant is found by finding the difference between the diagonally down product and the diagonally up product


if D = $\left[\begin{array}{cc}a_1&a_2\\a_3&a_4\end{array}\right]$
So, D = $a_1 * a_4 - a_3 * a_2$

now ,
D = $\left[\begin{array}{cc}5&-2\\-3&1\end{array}\right]$

D = 5 * 1 - (-2) * (-3)

D = 5 - 6

D = -1