Question

Value of the determinant $\left|\begin{array}{ccc}1& 3& 5\\ 3& 4& 5\\ 0& 2& 3\end{array}\right|is$___

Answer 1

We have the determinant $\left|\begin{array}{ccc}1& 3& 5\\ 3& 4& 5\\ 0& 2& 3\end{array}\right|$

Since it's a 3 $\times$ determinant, we can use the Sarrus rule.

Sarrus rule includes writing the first two rows again after the last row

Now we just have to subtract the sum of product of diagonal entries coming from right to left from the same thing coming from left to right. So.

$\text{Determinant}=(1\times 4\times 3+3\times 2\times 5+0\times 3\times 5)-(5\times 4\times 0+5\times 2\times 1+3\times 3\times 3)=(12+30+0)-(0+10+27)=42-\left(37\right)=5\text{which is the correct answer}$