If A = frac{1}{2} begin{bmatrix} -1 & -sqrt{3 | vedclass

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

Question

(B) Given $A = \begin{bmatrix} -1/2 & -\sqrt{3}/2 \ \sqrt{3}/2 & -1/2 \end{bmatrix}$.This matrix is of the form $\begin{bmatrix} \cos(240^\circ) & -\

Vedclass · Accepted Answer

a unit matrix

Vedclass · Answer

(B) Given $A = \begin{bmatrix} -1/2 & -\sqrt{3}/2 \ \sqrt{3}/2 & -1/2 \end{bmatrix}$.This matrix is of the form $\begin{bmatrix} \cos(240^\circ) & -\sin(240^\circ) \ \sin(240^\circ) & \cos(240^\circ) \end{bmatrix}$, which is a rotation matrix $R_	heta$ with $	heta = 240^\circ = 4\pi/3$.For a rotation matrix, $A^{-1} = R_{-	heta}$ and $A^2 = R_{2	heta}$.$A^{-1} = \begin{bmatrix} \cos(120^\circ) & -\sin(120^\circ) \ \sin(120^\circ) & \cos(120^\circ) \end{bmatrix} = \begin{bmatrix} -1/2 & -\sqrt{3}/2 \ \sqrt{3}/2 & -1/2 \end{bmatrix}$.$A^2 = \begin{bmatrix} \cos(480^\circ) & -\sin(480^\circ) \ \sin(480^\circ) & \cos(480^\circ) \end{bmatrix} = \begin{bmatrix} \cos(120^\circ) & -\sin(120^\circ) \ \sin(120^\circ) & \cos(120^\circ) \end{bmatrix} = \begin{bmatrix} -1/2 & -\sqrt{3}/2 \ \sqrt{3}/2 & -1/2 \end{bmatrix}$.Thus, $A^{-1} - A^2 = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$, which is a null matrix.$A$ null matrix is also a diagonal matrix and a scalar matrix, but it is not a unit matrix.

If $A = \frac{1}{2} \begin{bmatrix} -1 & -\sqrt{3} \\ \sqrt{3} & -1 \end{bmatrix}$, then $A^{-1} - A^2$ is not:

Similar Questions

If $A = \begin{bmatrix} 2 & -2 \\ 4 & 3 \end{bmatrix}$,then $A^{-1} =$

If $3 A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}$ and $A A^{T} = I$,then find the value of $\frac{a}{b} + \frac{b}{a}$.

The adjoint of $\begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3 \end{bmatrix}$ is

If $A = \begin{bmatrix} 8 & -2 \\ -4 & 1 \end{bmatrix}$ is given,then $A^{-1}$ is:

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ll}3 & 1 \\ 5 & 2\end{array}\right]$

Vedclass Test Series

Exam Paper Generator

Online Exam Module