Determinants

If $A=\left|\begin{array}{ccc}2& -3& 5\\ 6& 0& 4\\ 1& 5& -7\end{array}\right|$, then the cofactor of $a_{22}$ is _____.

If determinant of $Det\left(A\right)=4$, then determinant of its cofactors matrix is _____.

If $A_i, B_i, C_i$ are the cofactors of $a, b, c$ respectively , $i=1$ to $3$ in $\left|A\right|=\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_2& b_2& c_2\end{array}\right|$, show that $\left|\begin{array}{ccc}{A}_1& B_1& C_1\\ A_2& B_2& C_2\\ A_2& B_2& C_2\end{array}\right|={\left|A\right|}^2$

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

Check whether the following matrix is invertible or not:

$A=\left|\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right|$

If $A=\left|\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right|$, find the determinant of $\mathrm{Det}\left(A\right)$ of $A$ Sarrus Rule. Also check whether $A$ is invertible or not.

If $A=\left|\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right|$, then the determinant of $A$ is 

If $A=\left|\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right|$, then $\left|A\right|=$_____.  (Using Sarrus Rule).

If $A=\left|\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right|$, find determinants using Sarrus Rule.

If matrix $A=\left|\begin{array}{ccc}-8& -7& 6\\ -2& 1& 1\\ 0& 7& 7\end{array}\right|$, then $\left|A\right|=$_____. (Using the Laplace Expansion Equation).

If matrix $A=\left|\begin{array}{ccc}-8& -7& 6\\ -2& 1& 1\\ 0& 7& 7\end{array}\right|$, then calculate the determinant using the Laplace Expansion Equation.

For the matrix $A=\left|\begin{array}{ccc}12& 4& 19\\ 0& 0& 1\\ 37& 2& 5\end{array}\right|$

Calculate the determinant using the Laplace Expansion Equation with row $3$.

For the matrix $A=\left|\begin{array}{ccc}12& 4& 19\\ 0& 0& 1\\ 37& 2& 5\end{array}\right|$

Calculate the determinant using the Laplace Expansion Equation with row $2$.

For the matrix $A=\left|\begin{array}{ccc}12& 4& 19\\ 0& 0& 1\\ 37& 2& 5\end{array}\right|$

Calculate the determinant using the Laplace Expansion Equation with row $1$.

If $P=\left|\begin{array}{ccc}2& -3& 8\\ 21& 6& -6\\ 4& -33& 19\end{array}\right|$ and $Q=\left|\begin{array}{ccc}1& -29& -8\\ 2& 0& 3\\ 17& 15& 4\end{array}\right|$, then verify ${\left(P+Q\right)}^T=P^T+Q^T$.

If $P=\left|\begin{array}{ccc}2& -3& 8\\ 21& 6& -6\\ 4& -33& 19\end{array}\right|$ and $Q=\left|\begin{array}{ccc}1& -29& -8\\ 2& 0& 3\\ 17& 15& 4\end{array}\right|$, then find ${\left(P+Q\right)}^T=$?

If $A=\left|\begin{array}{cc}3& 4\\ 5& 6\end{array}\right|$ and $A^T=\left|\begin{array}{cc}3& 5\\ p& 6\end{array}\right|$, then the required value of $p$ is _____.

If $A=\left|\begin{array}{cc}1& 2\\ 3& 4\end{array}\right|$ and $A^T=\left|\begin{array}{cc}1& x\\ 2& 4\end{array}\right|$, then the required value of $x$ is

Find equation of line passing through points $\left(1,5\right) \& \left(4,3\right)$ using determinants.

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