IB Mathematics Applications & Interpretation Question Type 4: Finding the Determinant for a 2x2 Matrix Exercises

The vectors $\mathbf{u}=\left(\begin{array}{c}2\\ 3\end{array}\right)$ and $\mathbf{v}=\left(\begin{array}{c}1\\ 5\end{array}\right)$ form a parallelogram. Calculate its area.

Find the determinant of the matrix $A=\left(\begin{array}{cc}3& 5\\ 2& 7\end{array}\right)$.

Find the determinant of $B=\left(\begin{array}{cc}-4& 6\\ 3& -2\end{array}\right)$.

Determine all values of $k$ for which $F=\left(\begin{array}{cc}k+1& 4\\ 2& k-3\end{array}\right)$ is invertible.

Find the determinant of $C$.

Let $A=\left(\begin{array}{cc}2& 1\\ 0& 3\end{array}\right)$ and $B=\left(\begin{array}{cc}4& 5\\ 1& 2\end{array}\right)$. Compute $\det (A)$, $\det (B)$ and $\det (AB)$.

Compute the determinant of $H=\left(\begin{array}{cc}{t}^2& t\\ 2& 3t\end{array}\right)$ as a function of $t$.

Compute the determinant of $D=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)$ in terms of $a,b,c,d$.

If $A=\left(\begin{array}{cc}1& 2\\ 3& 4\end{array}\right)$, find $\det (3A)$.

Find the determinant of $G=\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right)$.

Given that $\det \left(\begin{array}{cc}2& x\\ 3& 5\end{array}\right)=7$, find $x$.

For the matrix $E=\left(\begin{array}{cc}k& 2\\ 5& k-1\end{array}\right)$, express $\det (E)$ in terms of $k$.