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If a = [ 2 3 5 7 ] , Find a + At. - Mathematics

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Question

If  \[A = \begin{bmatrix}2 & 3 \\ 5 & 7\end{bmatrix}\] , find A + AT.
 

 

Sum

Solution

\[Given: \hspace{0.167em} A = \begin{bmatrix}2 & 3 \\ 5 & 7\end{bmatrix} \] 

\[ A^T = \begin{bmatrix}2 & 5 \\ 3 & 7\end{bmatrix}\] 

\[Now, \] 

\[A + A^T = \begin{bmatrix}2 & 3 \\ 5 & 7\end{bmatrix} + \begin{bmatrix}2 & 5 \\ 3 & 7\end{bmatrix}\] 

\[ \Rightarrow A + A^T = \begin{bmatrix}2 + 2 & 3 + 5 \\ 5 + 3 & 7 + 7\end{bmatrix}\] 

\[ \Rightarrow A + A^T = \begin{bmatrix}4 & 8 \\ 8 & 14\end{bmatrix}\]

 

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Chapter 5: Algebra of Matrices - Exercise 5.6 [Page 62]

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RD Sharma Mathematics [English] Class 12
Chapter 5 Algebra of Matrices
Exercise 5.6 | Q 6 | Page 62

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