If A is a symmetric matrix and B is a skew-symmetrix matrix such … - Vidyadip

MCQ

If $A$ is a symmetric matrix and $B$ is a skew-symmetrix matrix such that $A + B = \left[ {\begin{array}{*{20}{c}}
2&3\\
5&{ - 1}
\end{array}} \right]$ , then $AB$ is equal to

A
$\left[ {\begin{array}{*{20}{c}}
4&{ - 2}\\
1&{ - 4}
\end{array}} \right]$
✓
$\left[ {\begin{array}{*{20}{c}}
4&{ - 2}\\
{ - 1}&{ - 4}
\end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{c}}
{ - 4}&2\\
1&4
\end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}}
{ - 4}&{ - 2}\\
{ - 1}&4
\end{array}} \right]$

✓

Answer

Correct option: B.

$\left[ {\begin{array}{*{20}{c}}
4&{ - 2}\\
{ - 1}&{ - 4}
\end{array}} \right]$

b
$A = A',B = B'$

$A + B = \left[ {\begin{array}{*{20}{c}}
2&3\\
5&{ - 1}
\end{array}} \right]\,\,\,\,\,\,\,\,....\left( 1 \right)$

$A' + B' = \left[ {\begin{array}{*{20}{c}}
2&5\\
3&{ - 1}
\end{array}} \right]\,\,\,$

$A - B = \left[ {\begin{array}{*{20}{c}}
2&5\\
3&{ - 1}
\end{array}} \right]\,\,\,\,\,\,\,\,.....\left( 2 \right)$

After addding equation $(1)$ and $(2)$

$A = \left[ {\begin{array}{*{20}{c}}
2&4\\
4&{ - 1}
\end{array}} \right]\,,B = \left[ {\begin{array}{*{20}{c}}
0&{ - 1}\\
1&0
\end{array}} \right]\,$

$AB = \left[ {\begin{array}{*{20}{c}}
4&{ - 2}\\
{ - 1}&{ - 4}
\end{array}} \right]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $S_n=\sum_{k=1}^n \frac{n}{n^2+k n+k^2}$ and $T_n=\sum_{k=0}^{n-1} \frac{n}{n^2+k n+k^2}$ for $n=1,2,3, \ldots$ Then,

$(A)$ $\mathrm{S}_{\mathrm{n}}<\frac{\pi}{3 \sqrt{3}}$ $(B)$ $S_n>\frac{\pi}{3 \sqrt{3}}$

$(C)$ $T_n<\frac{\pi}{3 \sqrt{3}}$ $(D)$ $T_n>\frac{\pi}{3 \sqrt{3}}$

Fifteen football players of a club-team are given $15$ T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least $3$ players pick the correct $T$-shirt is

Let $\text{A}=\begin{bmatrix}\text{a}&0&0\\0&\text{a}&0\\0&0&\text{a}\end{bmatrix},$ then $A^n$ is equal to:

The degree of the differential equation $3\frac{{{d^2}y}}{{d{x^2}}} = {\left\{ {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} \right\}^{3/2}}$ is

If $P=\left[\begin{array}{ll}1 & 0 \\ 1 / 2 & 1\end{array}\right]$, then $P^{50}$ is:

If $\omega $ is an imaginary root of unity, then the value of $\left| {\,\begin{array}{*{20}{c}}a&{b{\omega ^2}}&{a\omega }\\{b\omega }&c&{b{\omega ^2}}\\{c{\omega ^2}}&{a\omega }&c\end{array}\,} \right|$ is

If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is:

If $\vec{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\vec b = \frac{1}{7}\left( {2 \hat{i} + 3 \hat{j} - 6 \hat{k}} \right)$,then the value of $\left( {2\vec a - \vec b} \right)\cdot\left[ {\left( {\vec a \times \vec b} \right) \times \left( {\vec a + 2\vec b} \right)} \right]$ is

Let f : $\text{R}-\{\frac{3}{5}\}\rightarrow\text{R}$ be defined by $\text{f(x)}=\frac{3\text{x}+2}{5\text{x}-2}.$ Then:

Let $b = 4i + 3j$ and c be two vectors perpendicular to each other in the $xy-$ plane. All vectors in the same plane having projections $1$ and $2 $ along $b $ and $c$ respectively, are given by