If A=left[begin{array}{lll}3 & √{3} & 2 4 & 2 & 0end{array}right] and B=left[begin

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3 and 4 .Determinants and Matrices

easy

If $A=\left[\begin{array}{lll}3 & \sqrt{3} & 2 \\ 4 & 2 & 0\end{array}\right]$ and $B=\left[\begin{array}{rrr}2 & -1 & 2 \\ 1 & 2 & 4\end{array}\right],$ verify that $\left(\mathrm{A}^{\prime}\right)^{\prime}=\mathrm{A}$.

Option A

Option B

Option C

Option D

Solution

We have

$A=\left[\begin{array}{lll}3 & \sqrt{3} & 2 \\ 4 & 2 & 0\end{array}\right]$ $\Rightarrow A^{\prime}=\left[\begin{array}{ll}3 & 4 \\ \sqrt{3} & 2 \\ 2 & 0\end{array}\right] \Rightarrow$ $\left(\mathrm{A}^{\prime}\right)^{\prime}=\left[\begin{array}{lll}3 & \sqrt{3} & 2 \\ 4 & 2 & 0\end{array}\right]=\mathrm{A}$

Thus $\left(A^{\prime}\right)^{\prime}=A$

Standard 12

Mathematics

Express the following matrices as the sum of a symmetric and a skew symmetric matrix : $\left[\begin{array}{cc}3 & 5 \\ 1 & -1\end{array}\right]$

medium

If $A = \left( {\begin{array}{{20}{c}}
2&{ – 1}\\
{ – 7}&4
\end{array}} \right)$ and $B = \left( {\begin{array}{{20}{c}}
4&1\\
7&2
\end{array}} \right)$ then which of the following is correct

normal

If $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right],$ then verify that $A^{\prime} A=I$

medium

Assuming that the sums and products given below are defined, which of the following is not true for matrices

normal

Find the transpose of the following matrices : $\left[\begin{array}{ccc}-1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1\end{array}\right]$