Single Choice

If $$I=I=\left[ \begin{matrix} 1 \\ 0 \end{matrix}\begin{matrix} 0 \\ 1 \end{matrix} \right] ,j=\left[ \begin{matrix} 0 \\ -1 \end{matrix}\begin{matrix} 1 \\ 0 \end{matrix} \right] and B=\left[ \begin{matrix} cos\theta \\ -sin\theta \end{matrix}\begin{matrix} sin\theta \\ cos\theta \end{matrix} \right] ,$$ then B =

A$$Icos\theta +Jsin\theta $$
Correct Answer
B$$Icos\theta -Jsin\theta $$
C$$Isin\theta +Jcos\theta $$
D$$-Icos\theta +Jsin\theta $$

Solution

Given, $$I=\begin{bmatrix} 1 & 0\\ 0 & 1\end{bmatrix}, J=\begin{bmatrix} 0 & 1\\ -1 & 0\end{bmatrix}$$ and $$B=\begin{bmatrix} \cos \theta &\sin\theta \\ -\sin\theta & \cos\theta\end{bmatrix}$$ $$=\cos\theta\begin{bmatrix} 1 & 0\\ 0 & 1\end{bmatrix} +\sin\theta \begin{bmatrix} 0 & 1\\ -1 & 0\end{bmatrix}$$ $$=I\cos\theta +J\sin\theta$$.

SIMILAR QUESTIONS

Matrices

Which of the following is the new row that results when you add rows $$1$$ and $$3$$? $$\begin{bmatrix}3&4&2&11\\9&1&0&0\\0&1&0&2\\0&0&6&1\end{bmatrix}$$

Matrices

Apply the elementary transformation of the following matrix. $$ B = \begin{bmatrix} 1 & -1 & 3 \\ 2 & 5 & 4 \end{bmatrix}, R_{1} \rightarrow R_{1} - R_{2} $$

Matrices

Find the inverse of the matrix $$A=\begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4 \end{bmatrix}$$ by using column transformations.

Matrices

Find inverse, by elementary row operations (if possible), of the following matrices $$\begin{bmatrix} 1 & -3 \\ -2 & 6 \end{bmatrix}$$

Matrices

If $$A = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 5 & 3 \\ 0 & 2 & 1 \end{bmatrix} $$ find $$A^{-1}$$, using elementary row transformations.

Contact Details