Question

Find the values of following determinants.
| 5 3|
| -7 0|

Answer 1

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

D = $\left[\begin{array}{cc}m_1&m_3\\m_2&m_4\end{array}\right]= m_1*m_4 - m_2*m_3$

here, D = $\left[\begin{array}{cc}5&3\\-7&0\end{array}\right]$

D = 5 * 0 - (-7 ) * 3

D = 0 + 21

D = 21

Answer 2

we know, if any determinant $\mathbb{A} = \left[\begin{array}{cc}a&b\\c&d\end{array}\right]$
Then, modulus of A = |A| = product of a and d - product of b and c = ad - bc

Here, given $\mathbb{A} = \left[\begin{array}{cc}5&3\\-7&0\end{array}\right]$
Then modulus of A = |A| = 5 × 0 - 3 × (-7) = 21
Hence, value of given determinant = 21