If A = begin{bmatrix} 1 & tan frac{alpha}{2} | vedclass

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

Question

(D) Given,$A = \begin{bmatrix} 1 & 	an \frac{\alpha}{2} \ -	an \frac{\alpha}{2} & 1 \end{bmatrix}$ and $AB = I$. Since $AB = I$,we have $B = A^{-1}

Vedclass · Accepted Answer

$\cos^2 \frac{\alpha}{2} \cdot A^T$

Vedclass · Answer

(D) Given,$A = \begin{bmatrix} 1 & 	an \frac{\alpha}{2} \ -	an \frac{\alpha}{2} & 1 \end{bmatrix}$ and $AB = I$. Since $AB = I$,we have $B = A^{-1}$. The determinant of $A$ is $|A| = (1)(1) - (	an \frac{\alpha}{2})(-	an \frac{\alpha}{2}) = 1 + 	an^2 \frac{\alpha}{2} = \sec^2 \frac{\alpha}{2}$. The adjoint of $A$ is $	ext{adj}(A) = \begin{bmatrix} 1 & -	an \frac{\alpha}{2} \ 	an \frac{\alpha}{2} & 1 \end{bmatrix}$. Thus,$A^{-1} = \frac{1}{|A|} 	ext{adj}(A) = \frac{1}{\sec^2 \frac{\alpha}{2}} \begin{bmatrix} 1 & -	an \frac{\alpha}{2} \ 	an \frac{\alpha}{2} & 1 \end{bmatrix}$. Since $\frac{1}{\sec^2 \frac{\alpha}{2}} = \cos^2 \frac{\alpha}{2}$,we get $B = \cos^2 \frac{\alpha}{2} \begin{bmatrix} 1 & -	an \frac{\alpha}{2} \ 	an \frac{\alpha}{2} & 1 \end{bmatrix}$. Note that $A^T = \begin{bmatrix} 1 & -	an \frac{\alpha}{2} \ 	an \frac{\alpha}{2} & 1 \end{bmatrix}$. Therefore,$B = \cos^2 \frac{\alpha}{2} \cdot A^T$.

If $A = \begin{bmatrix} 1 & \tan \frac{\alpha}{2} \\ -\tan \frac{\alpha}{2} & 1 \end{bmatrix}$ and $AB = I$,then $B$ is equal to

Similar Questions

Let $I$ be a unit matrix of order $6$. Let $A = (a_{ij})$ be a square matrix of order $6$ such that $a_{ij} = \begin{cases} 1, & \text{if } i+j=7 \\ 0, & \text{if } i+j \neq 7 \end{cases}$. Then $(A(\text{adj } A) A^{-1}) A^2 = $

If $X$ is a square matrix of order $3 \times 3$ and $\lambda$ is a scalar,then $adj(\lambda X)$ is equal to

Let $A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}$ and $B = I + \operatorname{adj}(A) + (\operatorname{adj} A)^2 + \dots + (\operatorname{adj} A)^{10}$. Then,the sum of all the elements of the matrix $B$ is:

Let $A = \begin{bmatrix} 1 & 2 \\ -5 & 1 \end{bmatrix}$ and $A^{-1} = xA + yI_2$,(where $I_2$ is the unit matrix of order $2$),then

Vedclass Test Series

Exam Paper Generator

Online Exam Module