Maharashtra Board Solutions for Chapter: Matrices, Exercise 3: Miscellaneous Exercise 2(A)

Check whether the following matrices are invertible or not $\left[\begin{array}{cc}2& 3\\ 10& 15\end{array}\right]$.

Check whether the following matrices are invertible or not $\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$.

Check whether the following matrices are invertible or not $\left[\begin{array}{ll}\sec \theta & \tan \theta \\ \tan \theta & \sec \theta \end{array}\right]$

Check whether the following matrices are invertible or not $\left[\begin{array}{lll}3& 4& 3\\ 1& 1& 0\\ 1& 4& 5\end{array}\right]$.

Check whether the following matrices are invertible or not $\left[\begin{array}{ccc}1& 2& 3\\ 2& -1& 3\\ 1& 2& 3\end{array}\right]$.

Check whether the following matrices are invertible or not $\left[\begin{array}{lll}1& 2& 3\\ 3& 4& 5\\ 4& 6& 8\end{array}\right]$.

Find $AB$, if $A=\left[\begin{array}{ccc}1& 2& 3\\ 1& -2& -3\end{array}\right]$ and $B=\left[\begin{array}{ll}1& -1\\ 1& 2\\ 1& -2\end{array}\right]$ Examine whether $AB$ has inverse or not.

  Find the inverse of the given matrix (if it exists)$\left[\begin{array}{ccc}1& -1& 2\\ 0& 2& -3\\ 3& -2& 4\end{array}\right]$