AP EAMCET · Maths · Matrices
\(\begin{aligned} & A(\alpha, \beta)=\left[\begin{array}{ccc}\cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & e^\beta\end{array}\right] \\ & \Rightarrow[A(\alpha, \beta)]^{-1}=\end{aligned}\)
- A \(A(-\alpha, \beta)\)
- B \(A(-\alpha,-\beta)\)
- C \(A(\alpha,-\beta)\)
- D \(A(\alpha, \beta)\)
Answer & Solution
Correct Answer
(B) \(A(-\alpha,-\beta)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, } A(\alpha, \beta)=\left[\begin{array}{rcc}\cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & e^\beta\end{array}\right] \\ & \text { Now, }|A(\alpha, \beta)|=e^\beta\left(\cos ^2 \alpha+\sin ^2 \alpha\right)=e^\beta \\ &…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\sin (x+y) \sec x \sec y=\)AP EAMCET 2022 Easy
- The straight line passing through \((-1,1)\) and remaining parallel to the line common to the pairs of lines provided by \(6 x^2-x y-12 y^2=0\) and \(15 x^2+14 x y-8 y^2=0\), isAP EAMCET 2022 Medium
- If a line is moving between the coordinate axes such that the sum of the intercepts made by it on the coordinate axes is always 12 , then the equation of that line which forms a triangle of maximum area with the coordinate axes isAP EAMCET 2023 Medium
- Area of the triangle formed by the lines \(3 x^2-4 x y+y^2=0,2 x-y=6\) isAP EAMCET 2004 Medium
- If \(\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+4 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\), \(\mathbf{c}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+4 \hat{\mathbf{k}}\) then, \(\left[\begin{array}{lll}\mathbf{a} \times \mathbf{b} & \mathbf{b} \times \mathbf{c} \quad \mathbf{c} \times \mathbf{a}\end{array}\right]=\)AP EAMCET 2020 Medium
- If and then the value of isAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- The maximum value of the modulus of \(e^{z^2}\) on the set \(\{z \in C / 0 \leq \operatorname{Re}(z) \leq 1,0 \leq \operatorname{Im}(z) \leq 1\}\) isAP EAMCET 2018 Medium
- In a plane electromagnetic wave, the maximum value of the electric field component is \(4.4 \mathrm{Vm}^{-1}\). The intensity of the wave is nearlyAP EAMCET 2022 Medium
- If a photocell is illuminated with a radiation of , the stopping potential is found to be ; then the work function of the emitter and the threshold wavelength are:AP EAMCET 2021 Medium
- If the determinant \(\left|\begin{array}{ccc}\cos 2 x & \sin ^2 x & \cos 2 x \\ \sin ^2 x & \cos 2 x & \cos ^2 x \\ \cos 2 x & \cos ^2 x & \cos 2 x\end{array}\right|\) is expanded in powers of \(\cos x\), then the constant term in the expansion isAP EAMCET 2021 Medium
- The line \(x=\frac{\pi}{4}\) divides the area of the region bounded by \(y=\sin x, y=\cos x\) and \(x\)-axis \(\left(0 \leq x \leq \frac{\pi}{2}\right)\) into two regions of areas \(A_1\) and \(A_2\). Then \(A_1, A_2\) equalsAP EAMCET 2009 Medium
- What is the depression of freezing point, when mole fraction of non-electrolyte solute in aqueous solution is \(0.01 ?\left(\mathrm{~K}_{\mathrm{f}}\right.\) of \(\left.\mathrm{H}_2 \mathrm{O}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\)AP EAMCET 2023 Medium