MCQ
If $A = \left[ \begin{array}{l}1\\2\\3\end{array} \right],$then $AA\ ' = $
- A$14$
- B$\left[ \begin{array}{l}1\\4\\3\end{array} \right]$
- ✓$\left[ {\begin{array}{*{20}{c}}1&2&3\\2&4&6\\3&6&9\end{array}} \right]$
- DNone of these
✓
Answer
Correct option: C.
$\left[ {\begin{array}{*{20}{c}}1&2&3\\2&4&6\\3&6&9\end{array}} \right]$
$A\ ' = [1\,\,2\,\,3],$
therefore $AA\ ' = \left[ \begin{array}{l}1\\2\\3\end{array} \right]\left[ {1\,\,2\,\,3} \right]$
$ = \left[ {\begin{array}{*{20}{c}}1&2&3\\2&4&6\\3&6&9\end{array}} \right]$.
therefore $AA\ ' = \left[ \begin{array}{l}1\\2\\3\end{array} \right]\left[ {1\,\,2\,\,3} \right]$
$ = \left[ {\begin{array}{*{20}{c}}1&2&3\\2&4&6\\3&6&9\end{array}} \right]$.
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 $^{{n^2} - n}{C_2}{ = ^{{n^2} - n}}{C_{10}}$, then $n = $
→${\tan ^{ - 1}}\frac{{1 - {x^2}}}{{2x}} + {\cos ^{ - 1}}\frac{{1 - {x^2}}}{{1 + {x^2}}} = $
→Let $\vec{a}=3 \hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{ c }=2 \hat{ i }-3 \hat{ j }+3 \hat{k}$. If $\vec{b}$ is $a$ vector such that $\vec{a}=\vec{b} \times \vec{c}$ and $|\vec{b}|^2=50$, then $|72-| \vec{b}+\left.\vec{c}\right|^2 \mid$ is equal to $..........$.
→In the $X Y$-plane, three distinct lines $l_1, l_2, l_3$ concur at a point $(\lambda, 0)$. Further the lines $l_1, l_2, l_3$ are normals to the parabola $y^2=6 x$ at the points $A=\left(x_1, y_1\right)$, $B=\left(x_2, y_2\right), C=\left(x_3, y_3\right)$ respectively. Then, we have
→A circle is drawn in a sector of a larger circle of radius $r$, as shown in the figure given below. The smaller circle is tangent to the two bounding radii and the arc of the sector. The radius of the small circle is
→Let $\mathrm{A}=\{1,2,3,4\}$ and $\mathrm{R}=\{(1,2),(2,3),(1,4)\}$ be a relation on $\mathrm{A}$. Let $\mathrm{S}$ be the equivalence relation on $A$ such that $\mathrm{R} \subset \mathrm{S}$ and the number of elements in $\mathrm{S}$ is $\mathrm{n}$. Then, the minimum value of $\mathrm{n}$ is...............
→If in a triangle $\overrightarrow {AB} = a,\,\,\overrightarrow {AC} = b$ and $ D, E $ are the mid-points of $ AB $ and $ AC$ respectively, then $\overrightarrow {DE} $ is equal to
→If $y = {(\sin x)^{\tan x}}$, then ${{dy} \over {dx}}$ is equal to
→The term independent of $x$ in the expansion of ${(1 + x)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is
→If $\omega ( \ne 1)$ is cube root of unity and ${(1 + \omega )^7} = A + B\omega $ ,then $A$ and $B$ equals
→