Determinant of a Square Matrix

The value of determinant $\left|\begin{array}{ccc}18& 40& 89\\ 40& 89& 198\\ 89& 198& 440\end{array}\right|$ is

If $a, b \& c$ are in A.P ., what would be the value of $\left|\begin{array}{ccc}x+1& x+2& x+a\\ x+2& x+3& x+b\\ x+3& x+4& x+c\end{array}\right|$

Let $A\left(x_1,y_1\right), B\left(x_2,y_2\right), C\left(x_3,y_3\right)$, then find the area of given triangle.

What is determinant?

If $x^2+y^2+z^2=1$, then find the Value of $\left|\begin{array}{lll}1& z& -y\\ -z& 1& x\\ y& -x& 1\end{array}\right|$ is

Find the value of determinant $\left|\begin{array}{cc}2& -4\\ -4& 2\end{array}\right|$

Find equation of line joining $(-3,4)$ and $(3,5)$ using determinants

Find equation of line joining $(-2,4)$ and $(2,5)$ using determinants

Find equation of line joining $(-1,1)$ and $(2,1)$ using determinants

Find equation of line joining $(3,1)$ and $(9,3)$ using determinants.

Find equation of line joining $(1,2)$ and $(3,6)$ using determinants

Find the cofactor of an element $a_{33}$ for the following determinant $\left|\begin{array}{ccc}2& 4& 5\\ 7& 1& 4\\ 1& 5& 8\end{array}\right|$.

Find the minor of an element $a_{33}$ for the following determinant $\left|\begin{array}{ccc}3& -3& 5\\ 6& 1& 4\\ 1& 5& -7\end{array}\right|$.

Find the minor of an element $a_{11}$ for the following determinant $\left|\begin{array}{ccc}3& -3& 5\\ 6& 1& 4\\ 1& 5& -7\end{array}\right|$.

Consider a matrix $A=\left(\begin{array}{ccc}1& 0& 0\\ 2& x& y\\ 4& 3& 5\end{array}\right)$ with integer entries and determinant $-5$. Then a possible value for $y$ is

Find the cofactor of an element $a_{12}$ for the following determinant $\left|\begin{array}{ccc}2& -3& 5\\ 6& 0& 4\\ 1& 5& -7\end{array}\right|$.