If A = left[ {begin{array}{*{20}{c}}1&{ - 2}5&3end{array}} right] , then A + {A^T} equals

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3 and 4 .Determinants and Matrices

easy

If $A = \left[ {\begin{array}{*{20}{c}}1&{ - 2}\\5&3\end{array}} \right]$, then $A + {A^T}$equals

$\left[ {\begin{array}{*{20}{c}}2&3\\3&6\end{array}} \right]$

$\left[ {\begin{array}{*{20}{c}}2&{ - 4}\\{10}&6\end{array}} \right]$

$\left[ {\begin{array}{*{20}{c}}2&4\\{ - 10}&6\end{array}} \right]$

None of these

Solution

(a) $A = \left[ {\begin{array}{*{20}{c}}1&{ – 2}\\5&3\end{array}} \right],\,$${A^T} = \left[ {\begin{array}{*{20}{c}}1&5\\{ – 2}&3\end{array}} \right],\,A + {A^T} = \left[ {\begin{array}{*{20}{c}}2&3\\3&6\end{array}} \right]$.

Standard 12

Mathematics

Let $A =\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]$ and $B =\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]$ such that
$AB = B$ and $a + d =2021,$ then the value of $ad – bc$ is equal to …… .

medium

(JEE MAIN-2021)

Match the Statements / Expressions in Column $I$ with the Statements / Expressions in Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.

Column $I$ Column $II$

$(A)$ The minimum value of $\frac{x^2+2 x+4}{x+2}$ is $(p)$ $0$

$(B)$ Let $A$ and $B$ be $3 \times 3$ matrices of real numbers, where $A$ is symmetric, $B$ is skewsymmetric, and $(A+B)(A-B)=(A-B)(A+B)$. If $(A B)^t=(-1)^k A B$, where $(A B)^t$ is the transpose of the matrix $A B$, then the possible values of $k$ are $(q)$ $1$

$(C)$ Let $\mathrm{a}=\log _3 \log _3 2$. An integer $\mathrm{k}$ satisfying $1<2^{\left(-k+3^{-2}\right)}<2$, must be less than $(r)$ $2$

$(D)$ If $\sin \theta=\cos \phi$, then the possible values of $\frac{1}{\pi}\left(\theta \pm \phi-\frac{\pi}{2}\right)$ are $(s)$ $3$

hard

(IIT-2008)

If $A = \left[ {\begin{array}{*{20}{c}}{\cos \theta }&{ – \sin \theta }\\{\sin \theta }&{\cos \theta }\end{array}} \right]$, then which of the following statements is not correct

easy

For any square matrix $A$, $A{A^T}$ is a

normal

The number of all $3 \times 3$ matrices $A$, with enteries from the set $\{-1,0,1\}$ such that the sum of the diagonal elements of $\mathrm{AA}^{\mathrm{T}}$ is $3,$ is

hard

(JEE MAIN-2020)

Column $I$	Column $II$
$(A)$ The minimum value of $\frac{x^2+2 x+4}{x+2}$ is	$(p)$ $0$
$(B)$ Let $A$ and $B$ be $3 \times 3$ matrices of real numbers, where $A$ is symmetric, $B$ is skewsymmetric, and $(A+B)(A-B)=(A-B)(A+B)$. If $(A B)^t=(-1)^k A B$, where $(A B)^t$ is the transpose of the matrix $A B$, then the possible values of $k$ are	$(q)$ $1$
$(C)$ Let $\mathrm{a}=\log _3 \log _3 2$. An integer $\mathrm{k}$ satisfying $1<2^{\left(-k+3^{-2}\right)}<2$, must be less than	$(r)$ $2$
$(D)$ If $\sin \theta=\cos \phi$, then the possible values of $\frac{1}{\pi}\left(\theta \pm \phi-\frac{\pi}{2}\right)$ are	$(s)$ $3$

If $A = \left[ {\begin{array}{*{20}{c}}1&{ - 2}\\5&3\end{array}} \right]$, then $A + {A^T}$equals

Solution

Similar Questions

Let $A =\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]$ and $B =\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]$ such that $AB = B$ and $a + d =2021,$ then the value of $ad – bc$ is equal to …… .

If $A = \left[ {\begin{array}{*{20}{c}}{\cos \theta }&{ – \sin \theta }\\{\sin \theta }&{\cos \theta }\end{array}} \right]$, then which of the following statements is not correct

For any square matrix $A$, $A{A^T}$ is a

The number of all $3 \times 3$ matrices $A$, with enteries from the set $\{-1,0,1\}$ such that the sum of the diagonal elements of $\mathrm{AA}^{\mathrm{T}}$ is $3,$ is

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Let $A =\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]$ and $B =\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]$ such that
$AB = B$ and $a + d =2021,$ then the value of $ad – bc$ is equal to …… .