Sample QuestionsMatrics questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $A^2=-\frac{1}{2}\left[\begin{array}{cc}1 & -4 \\ -1 & 2\end{array}\right]$ then $A=$
- A
$\left[\begin{array}{rr}2 & 4 \\ -1 & 1\end{array}\right]$
- B
$\left[\begin{array}{rr}2 & 4 \\ 1 & -1\end{array}\right]$
- C
$\left[\begin{array}{rr}2 & -4 \\ 1 & 1\end{array}\right]$
- ✓
$\left[\begin{array}{rr}2 & 4 \\ 1 & 1\end{array}\right]$
Answer: D.
View full solution →For a $2 \times 2$ matrix $A$, if $A(\operatorname{adj} A)=\left(\begin{array}{ll}10 & 0 \\ 0 & 10\end{array}\right)$ then determinant $A$ equals
Answer: B.
View full solution →The inverse of a symmetric matrix is
Answer: A.
View full solution →The inverse of $A=\left[\begin{array}{lll}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right]$
Answer: A.
View full solution →If $F(\alpha)=\left[\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{array}\right]$ where $\alpha \in R$ then $[F(\alpha)]^{-1}$ is =
Answer: A.
View full solution →Check whether the following matrices are invertible or not. : $\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 4 & 5 \\ 4 & 6 & 8\end{array}\right]$
View full solution →Check whether the following matrices are invertible or not. : $\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & -1 & 3 \\ 1 & 2 & 3\end{array}\right]$
View full solution →Check whether the following matrices are invertible or not. : $\left[\begin{array}{lll}3 & 4 & 3 \\ 1 & 1 & 0 \\ 1 & 4 & 5\end{array}\right]$
View full solution →Check whether the following matrices are invertible or not. : $\left[\begin{array}{rr}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$
View full solution →Check whether the following matrices are invertible or not. : $\left[\begin{array}{ll}2 & 3 \\ 10 & 15\end{array}\right]$
View full solution →if $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$ and $X$ is a $2 \times 2$ matrix such that $A X=1$, then find $X$.
View full solution →If $A=\left[\begin{array}{lll}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{array}\right]$ is a nonsingular matrix then find $A^{-1}$ by elementary row transformations. Hence, find the inverse of $\left[\begin{array}{ccc}2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{array}\right]$
View full solution →Find $A B$, if $A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 1 & -2 & -3\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & -1 \\ 1 & 2 \\ 1 & -2\end{array}\right]$ Examine whether $A B$ has inverse or not.
View full solution →Solve the following equations by the method of reduction. $x + 3y + 3z = 12, x + 4y + 4z = 15$ and $x + 3y + 4z = 13.$
View full solution →If $A=\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right]$, then find $A^{-1}$ by the adjoint method.
View full solution →If $A=\left[\begin{array}{lll}2 & 1 & 3 \\ 1 & 0 & 1 \\ 1 & 1 & 1\end{array}\right]$, then reduce it to $I_3$ by using row transformations.
View full solution →If $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 3 & 1\end{array}\right]$ then reduce it to $I_3$ by using column transformations.
View full solution →Find the inverse of each of the following matrices (if they exist) : $\left[\begin{array}{lll}1 & 2 & -2 \\ 0 & -2 & 1 \\ -1 & 3 & 0\end{array}\right]$
View full solution →Find the inverse of each of the following matrices $($if they exist$)$ : $\left[\begin{array}{lll}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$
View full solution →Find the inverse of each of the following matrices (if they exist) : $\left[\begin{array}{lll}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array}\right]$
View full solution →$a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{13} = |A|$
View full solution →$a_{11}A_{21} + a_{12}A_{22} + a_{13}A_{23} = 0$
View full solution →Solve the following equations by the method of reduction. $x + y + z = 1, 2x + 3y + 2z = 2$ and $x + y + 2z = 4.$
View full solution → Solve the following equations by the method of inversion $x – y + z = 4, 2x + y –3z = 0, x + y + z = 2.$
View full solution →Solve the equations $2x + 5y = 1 $ and $3x + 2y = 7$ by the method of inversion
View full solution →Solve the following equations by the methods of inversion : $5x – y +4z = 5, 2x + 3y + 5z = 2$ and $5x – 2y + 6z = -1$
View full solution →Solve the following equations by the methods of inversion : $x + y + z = 1, 2x + 3y + 2z = 2$ and $ax + ay + 2az = 4, a \neq 0.$
View full solution →Solve the following equations by the methods of inversion : $2x – y = -2 , 3x + 4y = 5$
View full solution →If $A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1\end{array}\right]$ and $B=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7\end{array}\right]$, then find a matrix $X$ such that $X A=B$.
View full solution →Find the inverse of $\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7\end{array}\right]$ by elementary row transformations.
View full solution →