# If t t t tt t t t t t t e e cos t e sin t A e e cos t e sin t e sin t e cos t e 2e sin t 2e cos t – – – – — – – é ù ê ú =- – – + – ë û then A is:

Question:

If

$$A=\left[\begin{array}{ccc} e^{t} & e^{-t} \cos t & e^{-t} \sin t \\ e^{t} & -e^{-t} \cos t-e^{-t} \sin t & -e^{-t} \sin t+e^{-t} \cos t \\ e^{t} & 2 e^{-t} \sin t & -2 e^{-t} \cos t \end{array}\right]$$

then $\mathrm{A}$ is:

1. invertible for all $t \in \mathbf{R}$.

2. invertible only if $t=\pi$.

3. not invertible for any $t \in \mathbf{R}$.

4. invertible only if $\mathrm{t}=\frac{\pi}{2}$.

Correct Option: 1

JEE Main Previous Year 1 Question of JEE Main from Mathematics Matrices and Determinants chapter.
JEE Main Previous Year Jan. 09, 2019 (II)

Solution:

### Related Questions

• Let $\theta=\frac{\pi}{5}$ and $A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$. If $\mathrm{B}=\mathrm{A}+\mathrm{A}^{4}$, then det (B):

View Solution

• If $\Delta=\left|\begin{array}{ccc}x-2 & 2 x-3 & 3 x-4 \\ 2 x-3 & 3 x-4 & 4 x-5 \\ 3 x-5 & 5 x-8 & 10 x-17\end{array}\right|=A x^{3}+B x^{2}+C x+D$ then $B+C$ is equal to :

View Solution

• Let $a-2 b+c=1$.

If $f(x)=\left|\begin{array}{lll}x+a & x+2 & x+1 \\ x+b & x+3 & x+2 \\ x+c & x+4 & x+3\end{array}\right|$

then :

View Solution

• If $\Delta_{1}=\left|\begin{array}{ccc}x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x\end{array}\right|$ and $\Delta_{2}=\left|\begin{array}{ccc}x & \sin 2 \theta & \cos 2 \theta \\ -\sin 2 \theta & -x & 1 \\ \cos 2 \theta & 1 & x\end{array}\right|, x \neq 0 ;$

then for all $\theta \in\left(0, \frac{\pi}{2}\right)$ :

View Solution

• The sum of the real roots of the equation

$\left|\begin{array}{ccc}x & -6 & -1 \\ 2 & -3 x & x-3 \\ -3 & 2 x & x+2\end{array}\right|=0$, is equal to:

View Solution

• Let $\mathrm{A}=\left[\begin{array}{ccc}2 & \mathrm{~b} & 1 \\ \mathrm{~b} & \mathrm{~b}^{2}+1 & \mathrm{~b} \\ 1 & \mathrm{~b} & 2\end{array}\right]$ where $\mathrm{b}>0$. Then the minimum

value of $\frac{\operatorname{det}(\mathrm{A})}{\mathrm{b}}$ is:

View Solution

• If $\left|\begin{array}{lll}x-4 & 2 x & 2 x \\ 2 x & x-4 & 2 x \\ 2 x & 2 x & x-4\end{array}\right|=(A+B x)(x-A)^{2}$, then the ordered pair $(A, B)$ is equal to :

View Solution

• If $S=\left\{x \in[0,2 \pi]:\left|\begin{array}{ccc}0 & \cos x & -\sin x \\ \sin x & 0 & \cos x \\ \cos x & \sin x & 0\end{array}\right|=0\right\}$, then $\sum_{x \in S} \tan \left(\frac{\pi}{3}+x\right)$ is equal to

View Solution

• If $\mathrm{A}=\left[\begin{array}{cc}-4 & -1 \\ 3 & 1\end{array}\right]$, then the determinant of the matrix $\left(A^{2016}-2 A^{2015}-A^{2014}\right)$ is :

View Solution

• $\left|\begin{array}{ccc}x^{2}+x & x+1 & x-2 \\ 2 x^{2}+3 x-1 & 3 x & 3 x-3 \\ x^{2}+2 x+3 & 2 x-1 & 2 x-1\end{array}\right|=a x-12$, then ‘ $a$ ‘ is equal to :

View Solution

error: Content is protected !!