Embibe Experts Solutions for Chapter: Matrices, Exercise 1: Exercise

Identify scalar matrix from the following matrices.

Which of the following represents a zero matrix?

Which of the following represents a row matrix?

Which of the following represents a column matrix? 

If $A=\left[\begin{array}{l}1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-1\\ 2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-1\end{array}\right]$ and $B=\left[\begin{array}{r}a \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\\ b\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-1\end{array}\right]$ and $(A+B{)}^2=\left(A^2+B^2\right)$ then 

If $A=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{array}\right]$, and $A+A^{\text{'}}=I$, then the value of $\alpha$ is

If $\mathrm{A}=\left[\begin{array}{ll}3& -2\\ 4& -2\end{array}\right]$ and ${\mathrm{A}}^2-k\mathrm{A}+2\mathrm{I}=\mathrm{O}$, then $k=$

Assertion(A) : If $A$ is invertible square matrix, then $A^T$  is invertible

Reason(R) : Inverse of invertible symmetric matrix is symmetric matrix.

Choose the correct option: