Question
Find if $\begin{aligned} &\left[\begin{array}{c}\sin \theta \\ \cos \theta \\ \theta\end{array}\right]\left[\begin{array}{lll}\sin \theta & \cos \theta & \theta\end{array}\right]=[17] \end{aligned}$
✓
Answer
Let $\left[\begin{array}{c}\sin \theta \\ \cos \theta \\ \theta\end{array}\right]\left[\begin{array}{lll}\sin \theta & \cos \theta & \theta\end{array}\right]=[17],$
$\therefore\left[\sin ^2 \theta+\cos ^2 \theta+\theta^2\right]=[17]$
$\therefore$ By definition of equality of matries
$ \therefore 1+\theta=17 $
$\therefore \theta=17-1 $
$\therefore \theta^2=16,$
$\therefore \theta= \pm 4$
$\therefore\left[\sin ^2 \theta+\cos ^2 \theta+\theta^2\right]=[17]$
$\therefore$ By definition of equality of matries
$ \therefore 1+\theta=17 $
$\therefore \theta=17-1 $
$\therefore \theta^2=16,$
$\therefore \theta= \pm 4$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $A=\left[\begin{array}{ll}2 & -1 \\ 3 & -2\end{array}\right]$, find $A^3$.
→Find the equation of the line : passing through the point $\mathrm{N}(-2,3)$ and the segment of the line intercepted between the co-ordinate axes is bisected at $\mathrm{N}$.
→Show that following pairs of lines are perpendicular to each other : $y=2 x+23$ and $2 x+4 y=27$
→Find the acute angle between lines having slopes 3 and −2.
Find the co-ordinates of the point of intersection of lines $x+2 y=3$ and $2 x-y=1$.
→Obtain the equation of the line which is: parallel to the X-axis and 3 units below it.
If $A=\left[\begin{array}{ccc}4 & 3 & 2 \\ -1 & 2 & 0\end{array}\right], B=\left[\begin{array}{cc}1 & 2 \\ -1 & 0 \\ 1 & -2\end{array}\right]$, show that matrix $A B$ is non singular.
→Given below is the frequency distribution of weekly wages of 400 workers. Find the range.
Does point A(2, 3) lie on the line 3x + 2y – 6 = 0? Give reason.
Classify the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew- symmetric matrix :
→$\left[\begin{array}{ll}6 & 0 \\ 0 & 6\end{array}\right]$