If A_alpha = begin{bmatrix} cos alpha & sin a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given $A_\alpha = \begin{bmatrix} \cos \alpha & \sin \alpha \ -\sin \alpha & \cos \alpha \end{bmatrix}$.The determinant of matrix $A_\alpha$ is $

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) Given $A_\alpha = \begin{bmatrix} \cos \alpha & \sin \alpha \ -\sin \alpha & \cos \alpha \end{bmatrix}$.The determinant of matrix $A_\alpha$ is $\det(A_\alpha) = \cos^2 \alpha - (-\sin^2 \alpha) = \cos^2 \alpha + \sin^2 \alpha = 1$.We know that for any square matrices $A$ and $B$, $\det(AB) = \det(A) \cdot \det(B)$.Therefore, $\det(A_{\pi / 5} A_{\pi / 4} A_{3 \pi / 10}) = \det(A_{\pi / 5}) \cdot \det(A_{\pi / 4}) \cdot \det(A_{3 \pi / 10})$.Since $\det(A_\alpha) = 1$ for any value of $\alpha$, we have $\det(A_{\pi / 5}) = 1$, $\det(A_{\pi / 4}) = 1$, and $\det(A_{3 \pi / 10}) = 1$.Thus, $\det(A_{\pi / 5} A_{\pi / 4} A_{3 \pi / 10}) = 1 	imes 1 	imes 1 = 1$.

If $A_\alpha = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}$, then the determinant of $A_{\pi / 5} A_{\pi / 4} A_{3 \pi / 10}$ is:

Similar Questions

$\left|\begin{array}{ccc}\frac{-bc}{a^2} & \frac{c}{a} & \frac{b}{a} \\ \frac{c}{b} & \frac{-ac}{b^2} & \frac{a}{b} \\ \frac{b}{c} & \frac{a}{c} & \frac{-ab}{c^2}\end{array}\right| = $

If $\left| {\begin{array}{*{20}{c}}{{x^2} + x}&{x + 1}&{x - 2}\\ {2{x^2} + 3x - 1}&{3x}&{3x - 3}\\ {{x^2} + 2x + 3}&{2x - 1}&{2x - 1}\end{array}} \right| = Ax - 12$,then the value of $A$ is

Area of the triangle formed by points $(102, -4)$,$(105, -2)$,and $(103, -3)$ is:

If $a, b, c$ are positive and unequal,show that the value of the determinant $\Delta = \begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$ is negative.

If the system of equations $(\alpha + 1)^3 x + (\alpha + 2)^3 y - (\alpha + 3)^3 = 0$,$(\alpha + 1)x + (\alpha + 2)y - (\alpha + 3) = 0$,and $x + y - 1 = 0$ is consistent,what is the value of $\alpha$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module